List of mathematical constants

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems.{{Cite web|last=Weisstein|first=Eric W.|title=Constant|url=https://mathworld.wolfram.com/Constant.html|access-date=2020-08-08|website=mathworld.wolfram.com|language=en}} For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery.

The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them.

List

class="wikitable sortable sticky-header sort-under"
rowspan="2" \| Name ! rowspan="2" \| Symbol ! rowspan="2" \| Decimal expansion ! rowspan="2" \| Formula ! rowspan="2" \| Year ! colspan="3" \| Set
$\mathbb{Q}$ ! $\mathbb{A}$ ! $\mathcal{P}$
One \|1 \|1 \|Multiplicative identity of $\mathbb{C}$ . \| data-sort-value="-2000" \|Prehistory \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Two \|2 \|2 \| \| data-sort-value="-2000" \|Prehistory \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
One half \|{{sfrac\|1\|2}} \| data-sort-value="0.50000" \|0.5 \| \| data-sort-value="-2000" \|Prehistory \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Pi \| $\pi$ \|3.14159 26535 89793 23846 {{MathWorld\|PiFormulas\|Pi Formulas}}{{OEIS2C\|A000796}} \|Ratio of a circle's circumference to its diameter. \| data-sort-value="-1900" \|1900 to 1600 BCE {{harvnb\|Arndt\|Haenel\|2006\|p=167}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Tau \| $\tau$ \|6.28318 53071 79586 47692{{cite web \|last1=Hartl \|first1=Michael \|title=100,000 digits of Tau \|url=https://tauday.com/tau-digits \|website=Tau Day \|access-date=22 January 2023}}{{OEIS2C\|A019692}} \|Ratio of a circle's circumference to its radius. Equal to $2\pi$ \| data-sort-value="-1900" \|1900 to 1600 BCE {{harvnb\|Arndt\|Haenel\|2006\|p=167}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Square root of 2, Pythagoras constant{{cite book\|title=Mathematical sorcery: revealing the secrets of numbers\|author=Calvin C Clawson\|year=2001\|isbn=978 0 7382 0496-3\|page=IV\|publisher=Basic Books}} \| $\sqrt{2}$ \|1.41421 35623 73095 04880 {{MathWorld\|PythagorassConstant\|Pythagoras's Constant}}{{OEIS2C\|A002193}} \|Positive root of $x^2=2$ \| data-sort-value="-1800" \|1800 to 1600 BCEFowler and Robson, p. 368. [http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection] {{webarchive\|url=https://web.archive.org/web/20120813054036/http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html\|date=2012-08-13}} [http://www.math.ubc.ca/%7Ecass/Euclid/ybc/ybc.html High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection] \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Square root of 3, Theodorus' constant{{cite book\|url=https://books.google.com/books?id=xAwukpHCqH0C&q=1.732050807&pg=PA15\|title=Figuring Out Mathematics\|author=Vijaya AV\|publisher=Dorling Kindcrsley (India) Pvt. Lid.\|year=2007\|isbn=978-81-317-0359-5\|page=15}} \| $\sqrt{3}$ \|1.73205 08075 68877 29352 {{MathWorld\|TheodorussConstant\|Theodorus's Constant}}{{OEIS2C\|A002194}} \|Positive root of $x^2=3$ \| data-sort-value="-465" \|465 to 398 BCE \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Square root of 5{{cite book\|url=https://books.google.com/books?id=KjMVx6ljh6YC&q=2.236067977&pg=PA24\|title=Essential Mathematics 9\|author=P A J Lewis\|publisher=Ratna Sagar\|year=2008\|isbn=9788183323673\|page=24}} \| $\sqrt{5}$ \|2.23606 79774 99789 69640 {{OEIS2C\|A002163}} \|Positive root of $x^2=5$ \| data-sort-value="-464" \| \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Phi, Golden ratio{{cite book\|url=https://books.google.com/books?id=ZOfUsvemJDMC&q=1.618033988749894848&pg=PA316\|title=The Princeton Companion to Mathematics\|author1=Timothy Gowers\|author2=June Barrow-Green\|author3=Imre Leade\|publisher=Princeton University Press\|year=2007\|isbn=978-0-691-11880-2\|page=316}} \| $\varphi$ or $\phi$ \|1.61803 39887 49894 84820 {{MathWorld\|GoldenRatio\|Golden Ratio}}{{OEIS2C\|A001622}} \| $\frac{1+\sqrt{5}}{2}$ \| data-sort-value="-301" \|~300 BCE \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Silver ratio{{citation\|last=Kapusta\|first=Janos\|title=The square, the circle, and the golden proportion: a new class of geometrical constructions\|journal=Forma\|volume=19\|year=2004\|pages=293–313\|url=http://www.scipress.org/journals/forma/pdf/1904/19040293.pdf\|access-date=2022-01-28\|archive-date=2020-09-18\|archive-url=https://web.archive.org/web/20200918165840/http://www.scipress.org/journals/forma/pdf/1904/19040293.pdf\|url-status=dead}}. \| $\delta_S$ \|2.41421 35623 73095 04880 {{MathWorld\|SilverRatio\|Silver Ratio}}{{OEIS2C\|A014176}} \| $\sqrt{2}+1$ \| data-sort-value="-301" \|~300 BCE \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Zero \|0 \|0 \|Additive identity of $\mathbb{C}$ . \| data-sort-value="-300" \|300 to 100 BCEKim Plofker (2009), Mathematics in India, Princeton University Press, {{ISBN\|978-0-691-12067-6}}, pp. 54–56. \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Negative one \| −1 \| −1 \| \| data-sort-value="-300" \|300 to 200 BCE \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Cube root of 2 \| $\sqrt[3]{2}$ \|1.25992 10498 94873 16476 {{MathWorld\|DelianConstant\|Delian Constant}}{{OEIS2C\|A002580}} \|Real root of $x^3=2$ \|46 to 120 CE{{cite book\|author=Plutarch\|title=Quaestiones convivales VIII.ii\|url=https://ebooks.adelaide.edu.au/p/plutarch/symposiacs/chapter8.html#section80\|section=718ef\|quote=And therefore Plato himself dislikes Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations\|access-date=2019-05-24\|archive-date=2009-11-19\|archive-url=https://web.archive.org/web/20091119061142/http://ebooks.adelaide.edu.au/p/plutarch/symposiacs/chapter8.html#section80\|url-status=dead}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Cube root of 3 \| $\sqrt[3]{3}$ \|1.44224 95703 07408 38232 {{OEIS2C\|A002581}} \|Real root of $x^3=3$ \| data-sort-value="47" \| \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Twelfth root of 2{{citation\|first=Thomas\|last=Christensen\|title=The Cambridge History of Western Music Theory\|year=2002\|page=[https://archive.org/details/cambridgehistory0000unse_t8n5/page/205 205]\|publisher=Cambridge University Press \|isbn=978-0521686983\|url=https://archive.org/details/cambridgehistory0000unse_t8n5/page/205}} \| $\sqrt[12]{2}$ \|1.05946 30943 59295 26456 {{OEIS2C\|A010774}} \|Real root of $x^{12}=2$ \| data-sort-value="47" \| \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Supergolden ratio{{cite book \|last1=Koshy \|first1=Thomas \|title=Fibonacci and Lucas Numbers with Applications \|date=2017 \|publisher=John Wiley & Sons \|isbn=9781118742174 \|edition=2 \|url=https://books.google.com/books?id=kAhCDwAAQBAJ&dq=supergolden+ratio%7Cnumber%7Cconstant&pg=PT523 \|accessdate=14 August 2018 \|language=en}} \| $\psi$ \|1.46557 12318 76768 02665 {{OEIS2C\|A092526}} \| $\frac{1 + \sqrt[3]{\frac{29 + 3\sqrt{93}}{2}} + \sqrt[3]{\frac{29 - 3\sqrt{93}}{2}}}{3}$ Real root of $x^{3} = x^{2} + 1$ \| data-sort-value="47" \| \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Imaginary unit{{cite book\|url=https://books.google.com/books?id=IKmMKOtSI50C&q=%22This+leads+to+some+amazing+results.+For+example,+Euler+discovered%22&pg=PA66\|title=Mathematics: The New Golden Age\|author=Keith J. Devlin\|publisher=Columbia University Press\|year=1999\|isbn=978-0-231-11638-1\|page=66}} \| $i$ \| data-sort-value="0" \|{{math\|0 + 1i}} \|Principal root of $x^2=-1$ {{refn\|group=nb\|Both {{math\|i}} and {{math\|−i}} are roots of this equation, though neither root is truly "positive" nor more fundamental than the other as they are algebraically equivalent. The distinction between signs of {{math\|i}} and {{math\|−i}} is in some ways arbitrary, but a useful notational device. See imaginary unit for more information.}} \|1501 to 1576 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Connective constant for the hexagonal lattice{{cite book\|url=http://www.labri.fr/perso/bousquet/Exposes/fpsac-saw.pdf\|title=Two-dimensional self-avoiding walks\|author=Mireille Bousquet-Mélou\|publisher=CNRS, LaBRI, Bordeaux, France\|author-link=Mireille Bousquet-Mélou}}{{cite book\|url=http://www.unige.ch/~smirnov/slides/slides-saw.pdf\|title=The connective constant of the honeycomb lattice √ (2 + √ 2)\|author1=Hugo Duminil-Copin\|author2=Stanislav Smirnov\|publisher=Université de Geneve\|year=2011\|name-list-style=amp}} \| $\mu$ \|1.84775 90650 22573 51225 {{MathWorld\|Self-AvoidingWalkConnectiveConstant\|Self-Avoiding Walk Connective Constant}}{{OEIS2C\|A179260}} \| $\sqrt{2 + \sqrt{2}}$ , as a root of the polynomial $x ^ 4-4 x ^ 2 + 2=0$ \|1593 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Kepler–Bouwkamp constant{{cite arXiv\|eprint=1301.6293\|class=math.MG\|author=Richard J. Mathar\|title=Circumscribed Regular Polygons\|year=2013}} \| $K'$ \|0.11494 20448 53296 20070 {{MathWorld\|PolygonInscribing\|Polygon Inscribing}}{{OEIS2C\|A085365}} \| $\prod_{n=3}^\infty \cos\left(\frac{\pi}{n} \right) = \cos\left(\frac{\pi}{3} \right) \cos\left(\frac{\pi}{4} \right) \cos\left(\frac{\pi}{5}\right) ...$ \|1596 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Wallis's constant \| \|2.09455 14815 42326 59148 {{MathWorld\|WallissConstant\|Wallis's Constant}}{{OEIS2C\|A007493}} \| $\sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}}$ Real root of $x^{3} - 2x - 5 = 0$ \|1616 to 1703 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Euler's number{{cite book\|url=https://books.google.com/books?id=zdBHMHV3m5YC&q=2.7182818284590452353602874&pg=PA76\|title=Mathematics and the Imagination\|author=E.Kasner y J.Newman.\|publisher=Conaculta\|year=2007\|isbn=978-968-5374-20-0\|page=77}} \| $e$ \|2.71828 18284 59045 23536 {{MathWorld\|e\|e}}{{OEIS2C\|A001113}} \| $\lim_{n \to \infty} \left( 1 + \frac {1}{n}\right)^n = \sum_{n=0}^{\infty}\frac{1}{n!} = 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} \cdots$ \|1618{{cite web\|url=http://www-history.mcs.st-and.ac.uk/HistTopics/e.html\|title=The number e\|last1=O'Connor\|first1=J J\|last2=Robertson\|first2=E F\|publisher=MacTutor History of Mathematics}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Natural logarithm of 2{{cite book\|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=0.6931471805599&pg=PA182\|title=Handbook of Continued Fractions for Special Functions\|author1=Annie Cuyt\|author1-link= Annie Cuyt \|author2=Vigdis Brevik Petersen\|author3=Brigitte Verdonk\|author4=Haakon Waadeland\|author5=William B. Jones\|publisher=Springer\|year=2008\|isbn=978-1-4020-6948-2\|page=182}} \| $\ln 2$ \|0.69314 71805 59945 30941 {{MathWorld\|NaturalLogarithmof2\|Natural Logarithm of 2}}{{OEIS2C\|A002162}} \|Real root of $e^{x} = 2$ $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} = \frac{1}{1} - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots$ \|1619{{cite book\|url=https://books.google.com/books?id=mGJRjIC9fZgC\|title=A History of Mathematics\|author-last=Cajori\|author-first=Florian\|date=1991\|publisher=AMS Bookstore\|isbn=0-8218-2102-4\|edition=5th\|page=152\|author-link=Florian Cajori}} & 1668 {{cite web\|url=http://www-history.mcs.st-and.ac.uk/HistTopics/e.html\|title=The number e\|author-last1=O'Connor\|author-first1=J. J.\|date=September 2001\|publisher=The MacTutor History of Mathematics archive\|access-date=2009-02-02\|author-first2=E. F.\|author-last2=Robertson}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Lemniscate constant{{cite book\|url=https://books.google.com/books?id=aKQhpm1h770C&q=2.6220575&pg=PA333\|title=L-Functions and Arithmetic\|author1=J. Coates\|author2=Martin J. Taylor\|publisher=Cambridge University Press\|year=1991\|isbn=978-0-521-38619-7\|page=333}} \| $\varpi$ \|2.62205 75542 92119 81046 {{MathWorld\|LemniscateConstant\|Lemniscate Constant}}{{OEIS2C\|A062539}} \| $2\int_{0}^1\frac{dt}{\sqrt{1-t^4}} = \frac14 \sqrt{\frac{2}{\pi}}\,\Gamma {\left(\frac14 \right)^2}$ Ratio of the perimeter of Bernoulli's lemniscate to its diameter. \|1718 to 1798 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Euler's constant \| $\gamma$ \|0.57721 56649 01532 86060 {{MathWorld\|Euler-MascheroniConstant\|Euler–Mascheroni Constant}}{{OEIS2C\|A001620}} \| $\lim_{n\to\infty}\left(-\log n + \sum_{k=1}^n \frac1{k}\right)=\int_1^\infty\left(-\frac1x+\frac1{\lfloor x\rfloor}\right)\,dx$ Limiting difference between the harmonic series and the natural logarithm. \|1735 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Erdős–Borwein constant{{cite arXiv\|eprint=0806.4410\|class=math.CA\|author=Robert Baillie\|title=Summing The Curious Series of Kempner and Irwin\|year=2013}} \| $E$ \|1.60669 51524 15291 76378 {{MathWorld\|Erdos-BorweinConstant\|Erdos-Borwein Constant}}{{OEIS2C\|A065442}} \| $\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} \! + \! \frac{1}{3} \! + \! \frac{1}{7} \! + \! \frac{1}{15} \! + \! \cdots$ \|1749{{cite book\|url=http://www.math.dartmouth.edu/~euler/pages/E190.html\|title=Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae\|author=Leonhard Euler\|year=1749\|page=108}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Omega constant \| $\Omega$ \|0.56714 32904 09783 87299 {{MathWorld\|OmegaConstant\|Omega Constant}}{{OEIS2C\|A030178}} \| $W(1)=\frac{1}{\pi}\int_0^\pi\log\left(1+\frac{\sin t}{t}e^{t\cot t}\right)dt$ where W is the Lambert W function \|1758 & 1783 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Apéry's constant{{cite book\|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=1.202056903159594285399738&pg=PA188\|title=Handbook of Continued Fractions for Special Functions\|author1=Annie Cuyt\|author2=Vigdis Brevik Petersen\|author3=Brigitte Verdonk\|author4=Haakon Waadelantl\|author5=William B. Jones.\|publisher=Springer\|year=2008\|isbn=978-1-4020-6948-2\|page=188}} \| $\zeta(3)$ \|1.20205 69031 59594 28539 {{MathWorld\|AperysConstant\|Apéry's Constant}}{{OEIS2C\|A002117}} \| $\zeta(3)=\sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots$ with the Riemann zeta function $\zeta(s)$ . \|1780 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="0" style="background:#a6ffa7;\|✓
Laplace limit{{cite book\|title=Orbital Mechanics for Engineering Students\|title-link=Orbital Mechanics for Engineering Students\|author=Howard Curtis\|publisher=Elsevier\|year=2014\|isbn=978-0-08-097747-8\|page=159}} \| \|0.66274 34193 49181 58097 {{MathWorld\|LaplaceLimit\|Laplace Limit}}{{OEIS2C\|A033259}} \|Real root of $\frac{ x e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1$ \| data-sort-value="1782" \|~1782 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Soldner constant{{cite book\|url=https://archive.org/details/bub_gb_g4Q_AAAAcAAJ\|title=Théorie et tables d'une nouvelle fonction transcendante\|author=Johann Georg Soldner\|publisher=J. Lindauer, München\|year=1809\|page=[https://archive.org/details/bub_gb_g4Q_AAAAcAAJ/page/n39 42]\|language=fr}}{{cite book\|url=https://archive.org/details/bub_gb_XkgDAAAAQAAJ\|title=Adnotationes ad calculum integralem Euleri\|author=Lorenzo Mascheroni\|publisher=Petrus Galeatius, Ticini\|year=1792\|page=[https://archive.org/details/bub_gb_XkgDAAAAQAAJ/page/n34 17]\|language=la}} \| $\mu$ \|1.45136 92348 83381 05028 {{MathWorld\|SoldnersConstant\|Soldner's Constant}}{{OEIS2C\|A070769}} \| $\mathrm{li}(x) = \int_0^x \frac{dt}{\ln t} = 0$ ; root of the logarithmic integral function. \|1792 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Gauss's constant{{cite book\|url=https://books.google.com/books?id=UrSnNeJW10YC&q=%22Gauss%27s+constant%22&pg=PA647\|title=An Atlas of Functions: With Equator, the Atlas Function Calculator\|author1=Keith B. Oldham\|author2=Jan C. Myland\|author3=Jerome Spanier\|publisher=Springer\|year=2009\|isbn=978-0-387-48806-6\|page=15}} \| $G$ \|0.83462 68416 74073 18628 {{MathWorld\|GausssConstant\|Gauss's Constant}}{{OEIS2C\|A014549}} \| $\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{1}{4\pi} \sqrt{\frac{2}{\pi}}\Gamma\left(\frac{1}{4}\right)^2=\frac \varpi\pi$ where agm is the arithmetic–geometric mean and $\varpi$ is the lemniscate constant. \|1799{{Cite book\|title=Undergraduate convexity : problems and solutions\|last=Nielsen, Mikkel Slot.\|date = July 2016\|isbn=9789813146211\|pages=162\|publisher=World Scientific \|oclc=951172848}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Second Hermite constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|title=Errata and Addenda to Mathematical Constants\|author=Steven Finch\|publisher=Harvard.edu\|year=2014\|access-date=2013-12-17\|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|archive-date=2016-03-16\|url-status=dead}} \| $\gamma_{2}$ \|1.15470 05383 79251 52901 {{MathWorld\|HermiteConstants\|Hermite Constants}}{{OEIS2C\|A246724}} \| $\frac{2}{\sqrt{3}}$ \|1822 to 1901 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Liouville's constant{{cite book\|title=Mathematical Traveler: Exploring the Grand History of Numbers\|author=Calvin C. Clawson\|publisher=Perseus\|year=2003\|isbn=978-0-7382-0835-0\|page=187}} \| $L$ \|0.11000 10000 00000 00000 0001 {{MathWorld\|LiouvillesConstant\|Liouville's Constant}}{{OEIS2C\|A012245}} \| $\sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}} + \cdots$ \| data-sort-value="1844" \|Before 1844 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
First continued fraction constant \| $C_1$ \|0.69777 46579 64007 98201 {{MathWorld\|ContinuedFractionConstants\|Continued Fraction Constants}}{{OEIS2C\|A052119}} \| $C_1=[0;1,2,3,4,5,...]=\frac{I_1(2)}{I_0(2)}$ , (see Bessel functions). $C_1\notin \mathbb A.$ {{Cite web \|last=Waldschmidt \|first=Michel \|date=2021 \|title=Irrationality and transcendence of values of special functions. \|url=https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/ValuesSpecialFunctions.pdf}} \|1855{{cite journal \|last1=Amoretti \|first1=F. \|title=Sur la fraction continue [0,1,2,3,4,...] \|journal=Nouvelles annales de mathématiques \|date=1855 \|volume=1 \|issue=14 \|pages=40–44 \|url=http://www.numdam.org/item/?id=NAM_1855_1_14__40_1}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Ramanujan's constant{{cite book\|url=https://books.google.com/books?id=txPhITLO1YoC&q=262537412640768743.99999999999925&pg=PA107\|title=Modular Forms: A Classical and Computational Introduction\|author=L. J. Lloyd James Peter Kilford\|publisher=Imperial College Press\|year=2008\|isbn=978-1-84816-213-6\|page=107}} \| \|262 53741 26407 68743 .99999 99999 99250 073 {{MathWorld\|RamanujanConstant\|Ramanujan Constant}}{{OEIS2C\|A060295}} \| $e^{\pi\sqrt{163}}$ \|1859 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Glaisher–Kinkelin constant \| $A$ \|1.28242 71291 00622 63687 {{MathWorld\|Glaisher-KinkelinConstant\|Glaisher-Kinkelin Constant}}{{OEIS2C\|A074962}} \| $e^{\frac{1}{12}-\zeta^\prime(-1)} = e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^\infty \frac{1}{n+1} \sum\limits_{k=0}^n \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)}$ \|1860 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Catalan's constant{{cite book\|url=https://books.google.com/books?id=5Lp-tGZR25sC&q=0.91596559417721901505460351493238411&pg=PA127\|title=Number Theory: Volume II: Analytic and Modern Tools\|author=Henri Cohen\|publisher=Springer\|year=2000\|isbn=978-0-387-49893-5\|page=127}}{{cite book\|url=https://books.google.com/books?id=NBcSzUlaWWAC&q=0.915965594177219015&pg=PA29\|title=Series Associated With the Zeta and Related Functions\|author1=H. M. Srivastava\|author2=Choi Junesang\|publisher=Kluwer Academic Publishers\|year=2001\|isbn=978-0-7923-7054-3\|page=30}}{{cite book\|url=https://books.google.com/books?id=LXZFAAAAcAAJ&pg=PA618\|title=Mémoire sur la transformation des séries, et sur quelques intégrales définies, Comptes rendus hebdomadaires des séances de l'Académie des sciences 59\|author=E. Catalan\|publisher=Kluwer Academic éditeurs\|year=1864\|page=618}} \| $G$ \|0.91596 55941 77219 01505 {{MathWorld\|CatalansConstant\|Catalan's Constant}}{{OEIS2C\|A006752}} \| $\beta(2)=\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^2} = \frac{1}{1^2}-\frac{1}{3^2} + \frac{1}{5^2} - \frac{1}{7^2} + \frac{1}{9^2} + \cdots$ with the Dirichlet beta function $\beta(s)$ . \|1864 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="0" style="background:#a6ffa7;\|✓
Dottie number{{cite book\|url=https://books.google.com/books?id=eztUxtCfNXoC&q=Single%20Variable%20Calculus%3A%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&pg=PA314\|title=Single Variable Calculus: Concepts and Contexts\|author=James Stewart\|publisher=Brooks/Cole\|year=2010\|isbn=978-0-495-55972-6\|page=314}} \| \|0.73908 51332 15160 64165 {{MathWorld\|DottieNumber\|Dottie Number}}{{OEIS2C\|A003957}} \|Real root of $\cos x = x$ \|1865 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Meissel–Mertens constant{{cite book\|url=https://books.google.com/books?id=7-sDtIy8MNIC&q=Khinchin%27s+constant&pg=PA161\|title=Gamma: Exploring Euler's Constant\|author=Julian Havil\|publisher=Princeton University Press\|year=2003\|isbn=9780691141336\|page=64}} \| $M$ \|0.26149 72128 47642 78375 {{MathWorld\|MertensConstant\|Mertens Constant}}{{OEIS2C\|A077761}} \| $\lim_{n\to\infty}\left(\sum_{p\le n}\frac{1}{p}-\ln\ln n\right) = \gamma + \sum_{p}\left(\ln\left(1 - \frac{1}{p}\right) + \frac{1}{p}\right)$ where γ is the Euler–Mascheroni constant and p is prime \|1866 & 1873 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Universal parabolic constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|title=Errata and Addenda to Mathematical Constants\|author=Steven Finch\|publisher=Harvard.edu\|year=2014\|page=59\|access-date=2013-12-17\|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|archive-date=2016-03-16\|url-status=dead}} \| $P$ \|2.29558 71493 92638 07403 {{MathWorld\|UniversalParabolicConstant\|Universal Parabolic Constant}}{{OEIS2C\|A103710}} \| $\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arsinh}(1)+\sqrt{2}$ \| data-sort-value="1891" \|Before 1891{{Cite book\|url=https://archive.org/details/anelementarytre00osbogoog\|title=An Elementary Treatise on the Differential and Integral Calculus\|last=Osborne\|first=George Abbott\|publisher=Leach, Shewell, and Sanborn\|year=1891\|pages=[https://archive.org/details/anelementarytre00osbogoog/page/n265 250]}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Cahen's constant{{cite book\|url=https://books.google.com/books?id=iAg8FL5jKSgC&q=%22cahen+constant%22&pg=PA72\|title=Series representations for some mathematical constants\|author=Yann Bugeaud\|year=2004\|isbn=978-0-521-82329-6\|page=72\|publisher=Cambridge University Press }} \| $C$ \|0.64341 05462 88338 02618 {{MathWorld\|CahensConstant\|Cahen's Constant}}{{OEIS2C\|A118227}} \| $\sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}$ where s_k is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ... \|1891 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Gelfond's constant{{cite book\|url=https://books.google.com/books?id=7L7xcjBPemEC&q=23.14069&pg=RA2-PA4\|title=The Penguin Dictionary of Curious and Interesting Numbers\|author=David Wells\|author-link=David G. Wells\|publisher=Penguin Books Ltd.\|year=1997\|isbn=9780141929408\|page=4}} \| $e^{\pi}$ \|23.14069 26327 79269 0057 {{MathWorld\|GelfondsConstant\|Gelfonds Constant}}{{OEIS2C\|A039661}} \| $(-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = 1 + \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2} + \frac{\pi^{3}}{6} + \cdots$ \|1900{{cite book\|title=Mathematical Developments Arising from Hilbert Problems\|last=Tijdeman\|first=Robert\|publisher=American Mathematical Society\|year=1976\|isbn=0-8218-1428-1\|editor=Felix E. Browder\|editor-link=Felix Browder\|series=Proceedings of Symposia in Pure Mathematics\|volume=XXVIII.1\|pages=241–268\|chapter=On the Gel'fond–Baker method and its applications\|zbl=0341.10026\|author-link=Robert Tijdeman}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Gelfond–Schneider constant{{cite book\|url=https://books.google.com/books?id=RSU8AAAAQBAJ&q=2.6651&pg=PA328\|title=Precalculus: With Unit Circle Trigonometry\|author=David Cohen\|publisher=Thomson Learning Inc.\|year=2006\|isbn=978-0-534-40230-3\|page=328}} \| $2^{\sqrt{2}}$ \|2.66514 41426 90225 18865 {{MathWorld\|Gelfond-SchneiderConstant\|Gelfond-Schneider Constant}}{{OEIS2C\|A007507}} \| $2^{\sqrt{2}}$ \| data-sort-value="1902" \|Before 1902 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Second Favard constant{{cite book\|url=https://books.google.com/books?id=nbjOnJlJfFYC&q=Favard+Constant&pg=PA274\|title=Quadrature Theory: The Theory of Numerical Integration on a Compact Interval\|author1=Helmut Brass\|author2=Knut Petras\|publisher=AMS\|year=2010\|isbn=978-0-8218-5361-0\|page=274}} \| $K_{2}$ \|1.23370 05501 36169 82735 {{MathWorld\|FavardConstants\|Favard Constants}}{{OEIS2C\|A111003}} \| $\frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n+1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots$ \|1902 to 1965 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Golden angle{{cite book\|url=http://fibonacci.ucoz.com/index/ang/0-9\|title=Ángulo áureo}} \| $g$ \|2.39996 32297 28653 32223 {{MathWorld\|GoldenAngle\|Golden Angle}}{{OEIS2C\|A131988}} \| $\frac{2\pi}{\varphi^2} = \pi (3-\sqrt{5})$ or $180 (3-\sqrt{5})=137.50776\ldots$ in degrees \|1907 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Sierpiński's constant{{cite book\|url=https://books.google.com/books?id=aFDWuZZslUUC&q=1.584962500&pg=PA2685\|title=CRC Concise Encyclopedia of Mathematics, Second Edition\|author=Eric W. Weisstein\|publisher=CRC Press\|year=2002\|isbn=9781420035223\|page=1356}} \| $K$ \|2.58498 17595 79253 21706 {{MathWorld\|SierpinskiConstant\|Sierpinski Constant}}{{OEIS2C\|A062089}} \| $\begin{align} &\pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) = \pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi) \\ &= \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right) \end{align}$ \|1907 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Landau–Ramanujan constant{{cite book\|url=https://books.google.com/books?id=ZXjHKPS1LEAC&q=Landau-Ramanujan+constant&pg=PA80\|title=Prime Numbers: A Computational Perspective\|author1=Richard E. Crandall\|author2=Carl B. Pomerance\|publisher=Springer\|year=2005\|isbn=978-0387-25282-7\|page=80}} \| $K$ \|0.76422 36535 89220 66299 {{MathWorld\|Landau-RamanujanConstant\|Landau-Ramanujan Constant}}{{OEIS2C\|A064533}} \| $\frac1{\sqrt2}\prod_{{p \equiv 3 \text{ mod } 4}\atop p \;{\rm prime}} {\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{{p \equiv 1 \text{ mod } 4}\atop p \;{\rm prime}} {\left(1-\frac1{p^2}\right)^\frac{1}{2}}$ \|1908 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
First Nielsen–Ramanujan constant{{cite book\|url=http://bitman.name/math/article/872\|title=Nielsen – Ramanujan (costanti di)\|author=Mauro Fiorentini}} \| $a_{1}$ \|0.82246 70334 24113 21823 {{MathWorld\|Nielsen-RamanujanConstants\|Nielsen-Ramanujan Constants}}{{OEIS2C\|A072691}} \| $\frac{{\zeta}(2)}{2} = \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} {-} \frac{1}{2^2} {+} \frac{1}{3^2} {-} \frac{1}{4^2} {+} \cdots$ \|1909 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Gieseking constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf\|title=Volumes of Hyperbolic 3-Manifolds\|author=Steven Finch\|publisher=Harvard University\|archive-url=https://web.archive.org/web/20150919160427/http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf\|archive-date=2015-09-19\|url-status=dead}} \| $G$ \|1.01494 16064 09653 62502 {{MathWorld\|GiesekingsConstant\|Gieseking's Constant}}{{OEIS2C\|A143298}} \| $\frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)$ $=\frac{\sqrt 3}{3}\left(\frac{\psi_1(1/3)}{2}-\frac{\pi^2}{3}\right)$ with the trigamma function $\psi_1$ . \|1912 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="0" style="background:#a6ffa7;\|✓
Bernstein's constant{{cite book\|url=https://books.google.com/books?id=En41UGQ6YXsC&q=0.28016949902386913303643649&pg=PA211\|title=Approximation Theory and Approximation Practice\|author=Lloyd N. Trefethen\|publisher=SIAM\|year=2013\|isbn=978-1-611972-39-9\|page=211}} \| $\beta$ \|0.28016 94990 23869 13303 {{MathWorld\|BernsteinsConstant\|Bernstein's Constant}}{{OEIS2C\|A073001}} \| $\lim_{n\to\infty} 2n E_{2n}(f)$ , where E_n(f) is the error of the best uniform approximation to a real function f(x) on the interval [−1, 1] by real polynomials of no more than degree n, and f(x) = \|x\| \|1913 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Tribonacci constant{{Cite journal \|last=Agronomof \|first=M. \|year=1914 \|title=Sur une suite récurrente. \|journal=Mathesis \|volume=4 \|pages=125–126}} \| \|1.83928 67552 14161 13255 {{MathWorld\|TribonacciConstant\|Tribonacci Constant}}{{OEIS2C\|A058265}} \| $\frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3} = \frac{1+4\cosh\left(\frac{1}{3}\cosh^{-1}\left(2+\frac{3}{8}\right)\right)}{3}$ Real root of $x^{3} - x^{2} - x - 1 = 0$ \|1914 to 1963 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Brun's constant{{Cite book \|last=Thomas Koshy \|url=https://books.google.com/books?id=d5Z5I3gnFh0C&q=Brun+constant&pg=PA118 \|title=Elementary Number Theory with Applications \|publisher=Elsevier \|year=2007 \|isbn=978-0-12-372-487-8 \|page=119}} \| $B_{2}$ \|1.90216 05831 04 {{refn\|group=Mw\|name=Brun's Constant\|{{MathWorld\|BrunsConstant\|Brun's Constant}}}}{{OEIS2C\|A065421}} \| $\textstyle {\sum\limits_p(\frac1{p}+\frac1{p+2})} = (\frac1{3} \! + \! \frac1{5}) + (\tfrac1{5} \! + \! \tfrac1{7}) + (\tfrac1{11} \! + \! \tfrac1{13}) + \cdots$ where the sum ranges over all primes p such that p + 2 is also a prime \|1919 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Twin primes constant \| $C_{2}$ \|0.66016 18158 46869 57392 {{MathWorld\|TwinPrimesConstant\|Twin Primes Constant}}{{OEIS2C\|A005597}} \| $\prod_{\textstyle{p\;{\rm prime}\atop p \ge 3}} \left(1 - \frac{1}{(p-1)^2}\right)$ \|1922 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Plastic ratio{{cite book\|url=https://books.google.com/books?id=oW6Xeo8EmDgC&q=%22Plastic+number%22&pg=PT120\|title=Professor Stewart's Cabinet of Mathematical Curiosities\|author=Ian Stewart\|publisher=Birkhäuser Verlag\|year=1996\|isbn=978-1-84765-128-0}} \| $\rho$ \|1.32471 79572 44746 02596 {{MathWorld\|PlasticConstant\|Plastic Constant}}{{OEIS2C\|A060006}} \| $\sqrt[3]{1 + \! \sqrt[3]{1 + \! \sqrt[3]{1 + \cdots}}} = \textstyle \sqrt[3]{\frac{1}{2}+\frac{\sqrt{69}}{18}}+\sqrt[3]{\frac{1}{2}-\frac{\sqrt{69}}{18}}$ Real root of $x^{3} = x + 1$ \|1924 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Bloch's constant{{cite book\|url=https://books.google.com/books?id=aFDWuZZslUUC&q=Bloch-Landau+constant&pg=PA1688\|title=CRC Concise Encyclopedia of Mathematics, Second Edition\|author=Eric W. Weisstein\|publisher=CRC Press\|year=2003\|isbn=978-1-58488-347-0\|page=1688}} \| $B$ \| data-sort-value="0.43320" \| $0.4332\leq B\leq 0.4719$ {{MathWorld\|BlochConstant\|Bloch Constant}}{{OEIS2C\|A085508}} \|The best known bounds are $\frac{\sqrt{3}}{4}+2\times10^{-4}\leq B\leq \sqrt{\frac{\sqrt{3}-1}{2}}\cdot\frac{\Gamma(\frac{1}{3})\Gamma(\frac{11}{12})}{\Gamma(\frac{1}{4})}$ \|1925 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Z score for the 97.5 percentile point {{Citation\| last=Rees \| first=DG \|title=Foundations of Statistics\| page=246 \|publisher=CRC Press \|isbn=0-412-28560-6\| quote=Why 95% confidence? Why not some other confidence level? The use of 95% is partly convention, but levels such as 90%, 98% and sometimes 99.9% are also used.\| year=1987}}{{cite web \|url = http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm \|title = Engineering Statistics Handbook: Confidence Limits for the Mean \|accessdate = 2008-02-04 \|publisher = National Institute of Standards and Technology \|quote = Although the choice of confidence coefficient is somewhat arbitrary, in practice 90%, 95%, and 99% intervals are often used, with 95% being the most commonly used. \|archiveurl = https://web.archive.org/web/20080205120031/http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm \|archivedate = 5 February 2008 \|url-status = dead \|df = dmy-all }} {{Citation \| title=Real-Life Math: Statistics \| first1=Eric T \| last1=Olson \| first2=Tammy Perry \| last2=Olson \| page=[https://archive.org/details/statistics0000olso/page/66 66] \| publisher=Walch Publishing \| year=2000 \| isbn=0-8251-3863-9 \| quote=While other stricter, or looser, limits may be chosen, the 95 percent interval is very often preferred by statisticians. \| url=https://archive.org/details/statistics0000olso/page/66 }}{{cite journal\|doi=10.1080/03610920802255856\|last=Swift\| first=MB\| title=Comparison of Confidence Intervals for a Poisson Mean – Further Considerations\|journal=Communications in Statistics – Theory and Methods\|year=2009 \| volume=38\| issue=5\| pages=748–759\|s2cid=120748700 \| quote=In modern applied practice, almost all confidence intervals are stated at the 95% level.}} \| $z_{.975}$ \|1.95996 39845 40054 23552 {{MathWorld\|ConfidenceInterval\|Confidence Interval}}{{OEIS2C\|A220510}} \| $\sqrt{2}\operatorname{erf}^{-1}(0.95)$ where {{math\|erf⁻¹(x)}} is the inverse error function Real number $z$ such that $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{z} e^{-x^2/2} \, \mathrm{d}x = 0.975$ \|1925 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Landau's constant \| $L$ \| data-sort-value="0.50000" \| $0.5 < L \le 0.54326$ {{MathWorld\|LandauConstant\|Landau Constant}}{{OEIS2C\|A081760}} \|The best known bounds are $0.5 < L \le \frac{\Gamma(\frac{1}{3})\Gamma(\frac{5}{6})}{\Gamma(\frac{1}{6})}$ \|1929 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Landau's third constant \| $A$ \| data-sort-value="0.50000" \| $0.5 < A \le 0.7853$ \| \|1929 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Prouhet–Thue–Morse constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|title=Errata and Addenda to Mathematical Constants\|author=Steven Finch\|publisher=Harvard.edu\|year=2014\|page=53\|access-date=2013-12-17\|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf\|archive-date=2016-03-16\|url-status=dead}} \| $\tau$ \|0.41245 40336 40107 59778 {{MathWorld\|Thue-MorseConstant\|Thue-Morse Constant}}{{OEIS2C\|A014571}} \| $\sum_{n=0}^{\infty} \frac{t_n}{2^{n+1}} = \frac{1}{4}\left[2-\prod_{n=0}^{\infty}\left(1-\frac{1}{2^{2^n}}\right)\right]$ where ${t_n}$ is the n^th term of the Thue–Morse sequence \|1929 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Golomb–Dickman constant{{cite book\|url=https://books.google.com/books?id=aFDWuZZslUUC&q=Golomb%E2%80%93Dickman+constant&pg=PA1211\|title=CRC Concise Encyclopedia of Mathematics\|author=Eric W. Weisstein\|publisher=Crc Press\|year=2002\|isbn=9781420035223\|page=1212}} \| $\lambda$ \|0.62432 99885 43550 87099 {{MathWorld\|Golomb-DickmanConstant\|Golomb–Dickman Constant}}{{OEIS2C\|A084945}} \| $\int_{0}^{1} e^{\mathrm{Li}(t)} dt = \int_0^{\infty} \frac{\rho(t)}{t+2} dt$ where Li(t) is the logarithmic integral, and ρ(t) is the Dickman function \|1930 & 1964 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Constant related to the asymptotic behavior of Lebesgue constants{{cite journal\|author=Horst Alzer\|year=2002\|title=Journal of Computational and Applied Mathematics, Volume 139, Issue 2\|url=http://ac.els-cdn.com/S0377042701004265/1-s2.0-S0377042701004265-main.pdf?_tid=c20cf466-f4bf-11e3-bd9c-00000aacb362&acdnat=1402859198_57de7868bcc50086f092c66898ec6a33\|journal=Journal of Computational and Applied Mathematics\|volume=139\|issue=2\|pages=215–230\|doi=10.1016/S0377-0427(01)00426-5\|doi-access=free}} \| $c$ \|0.98943 12738 31146 95174 {{MathWorld\|LebesgueConstants\|Lebesgue Constants}}{{OEIS2C\|A243277}} \| $\lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=} \frac{4}{\pi^2}\!\left({-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}{+}{\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}} \right)$ \|1930 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Feller–Tornier constant{{cite book\|url=https://www.ams.org/journals/tran/1964-112-02/S0002-9947-1964-0166181-5/S0002-9947-1964-0166181-5.pdf\|title=SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS\|author=ECKFORD COHEN\|publisher=University of Tennessee\|year=1962\|page=220}} \| $\mathcal{C}_{\mathrm{FT}}$ \|0.66131 70494 69622 33528 {{MathWorld\|Feller-TornierConstant\|Feller–Tornier Constant}}{{OEIS2C\|A065493}} \| ${\frac{1}{2}\prod_{p\text{ prime}} \left(1-\frac{2}{p^2}\right) + \frac{1}{2}} =\frac{3}{\pi^2}\prod_{p\text{ prime}} \left(1-\frac{1}{p^2-1}\right) + \frac{1}{2}$ \|1932 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Base 10 Champernowne constant{{cite book\|url=https://books.google.com/books?id=wRWyMbmJTMYC&q=%22Champernowne+number%22&pg=PA109\|title=Computation, Physics and Beyond\|author1=Michael J. Dinneen\|author2=Bakhadyr Khoussainov\|author3=Prof. Andre Nies\|publisher=Springer\|year=2012\|isbn=978-3-642-27653-8\|page=110}} \| $C_{10}$ \|0.12345 67891 01112 13141 {{MathWorld\|ChampernowneConstant\|Champernowne Constant}}{{OEIS2C\|A033307}} \|Defined by concatenating representations of successive integers: 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... \|1933 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Salem constant{{cite book\|url=https://books.google.com/books?id=LYT5sBm_Ie0C&q=1.1762808&pg=PA246\|title=Distribution Theory of Algebraic Numbers\|author=Pei-Chu Hu, Chung-Chun\|publisher=Hong Kong University\|year=2008\|isbn=978-3-11-020536-7\|page=246}} \| $\sigma_{10}$ \|1.17628 08182 59917 50654 {{MathWorld\|SalemConstants\|Salem Constants}}{{OEIS2C\|A073011}} \|Largest real root of $x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1=0$ \|1933 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Khinchin's constant{{cite book\|url=https://books.google.com/books?id=7-sDtIy8MNIC&q=Khinchin%27s+constant&pg=PA161\|title=Gamma: Exploring Euler's Constant\|author=Julian Havil\|publisher=Princeton University Press\|year=2003\|isbn=9780691141336\|page=161}} \| $K_{0}$ \|{{nobr\|2.68545 20010 65306 44530}} {{MathWorld\|KhinchinsConstant\|Khinchin's Constant}}{{OEIS2C\|A002210}} \| $\prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\log_2(n)}$ \|1934 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Lévy's constant (1){{cite book\|url=https://books.google.com/books?id=R7Fp8vytgeAC&pg=PA66\|title=Continued Fractions\|author=Aleksandr I͡Akovlevich Khinchin\|publisher=Courier Dover Publications\|year=1997\|isbn=978-0-486-69630-0\|page=66}} \| $\beta$ \|1.18656 91104 15625 45282 {{MathWorld\|LevyConstant\|Levy Constant}}{{OEIS2C\|A100199}} \| $\frac {\pi^2}{12\,\ln 2}$ \|1935 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Lévy's constant (2){{cite journal\|arxiv=1002.4171\|author=Marek Wolf\|title=Two arguments that the nontrivial zeros of the Riemann zeta function are irrational\|journal=Computational Methods in Science and Technology\|year=2018\|volume=24\|issue=4\|pages=215–220\|doi=10.12921/cmst.2018.0000049\|s2cid=115174293}} \| $e^{\beta}$ \|3.27582 29187 21811 15978 {{MathWorld\|LevyConstant\|Levy Constant}}{{OEIS2C\|A086702}} \| $e^{\pi^2/(12\ln2)}$ \|1936 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Copeland–Erdős constant{{cite book\|url=https://books.google.com/books?id=NeEpoAf7k0IC&q=0.235711131719232931&pg=PA87\|title=Distribution Modulo One and Diophantine Approximation\|author=Yann Bugeaud\|publisher=Cambridge University Press\|year=2012\|isbn=978-0-521-11169-0\|page=87}} \| $\mathcal{C}_{CE}$ \|0.23571 11317 19232 93137 {{MathWorld\|Copeland-ErdosConstant\|Copeland–Erdos Constant}}{{OEIS2C\|A033308}} \|Defined by concatenating representations of successive prime numbers: 0.2 3 5 7 11 13 17 19 23 29 31 37 ... \|1946 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Mills' constant{{cite book\|title=Stealth Ciphers\|author=Laith Saadi\|publisher=Trafford Publishing\|year=2004\|isbn=978-1-4120-2409-9\|page=160}} \| $A$ \|1.30637 78838 63080 69046 {{MathWorld\|MillsConstant\|Mills Constant}}{{OEIS2C\|A051021}} \|Smallest positive real number A such that $\lfloor A^{3^{n}} \rfloor$ is prime for all positive integers n \|1947 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Gompertz constant{{cite book\|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=Gompertz+constant&pg=PA190\|title=Handbook of continued fractions for special functions\|author1=Annie Cuyt\|author2=Viadis Brevik Petersen\|author3=Brigitte Verdonk\|author4=William B. Jones\|publisher=Springer Science\|year=2008\|isbn=978-1-4020-6948-2\|page=190}} \| $\delta$ \|0.59634 73623 23194 07434 {{MathWorld\|GompertzConstant\|Gompertz Constant}}{{OEIS2C\|A073003}} \| $\int_0^\infty \!\! \frac{e^{-x}}{1+x} \, dx = \!\! \int_0^1 \!\! \frac{dx}{1-\ln x} = {\tfrac 1 {1+\tfrac 1{1+\tfrac 1{1+\tfrac 2{1+\tfrac 2{1+\tfrac 3{1+3{/\cdots}} }}}}}}$ \| data-sort-value="1948" \|Before 1948 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
de Bruijn–Newman constant \| $\Lambda$ \| data-sort-value="0" \| $0\le\Lambda\le0.2$ \|The number Λ such that $H(\lambda,z)=\int^{\infty}_0e^{\lambda u^2}\Phi(u)\cos(zu)du$ has real zeros if and only if λ ≥ Λ. where $\Phi(u)=\sum_{n=1}^{\infty}(2\pi^2n^4e^{9u}-3\pi n^2e^{5u})e^{-\pi n^2e^{4u}}$ . \|1950 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Van der Pauw constant \| $\frac{\pi}{\ln 2}$ \|4.53236 01418 27193 80962 {{OEIS2C\|A163973}} \| $\frac{\pi}{\ln 2}$ \| data-sort-value="1958" \|Before 1958 {{OEIS2C\|A163973}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Magic angle{{cite book\|url=https://books.google.com/books?id=WoaxgpHu19gC&q=0.955316&pg=PA150\|title=Discrete Geometry\|author=Andras Bezdek\|publisher=Marcel Dekkcr, Inc.\|year=2003\|isbn=978-0-8247-0968-6\|page=150}} \| $\theta_{\mathrm{m}}$ \|0.95531 66181 245092 78163 {{OEIS2C\|A195696}} \| $\arctan \sqrt{2} = \arccos \tfrac{1}{\sqrt 3} \approx \textstyle {54.7356} ^{ \circ }$ \| data-sort-value="1959" \|Before 1959 {{Cite journal\|last=Lowe\|first=I. J.\|date=1959-04-01\|title=Free Induction Decays of Rotating Solids\|url=https://link.aps.org/doi/10.1103/PhysRevLett.2.285\|journal=Physical Review Letters\|language=en\|volume=2\|issue=7\|pages=285–287\|doi=10.1103/PhysRevLett.2.285\|bibcode=1959PhRvL...2..285L \|issn=0031-9007}} \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Artin's constant{{cite book\|url=https://books.google.com/books?id=EiYvlcimEi4C&q=1.9287800&pg=PA66\|title=My Numbers, My Friends: Popular Lectures on Number Theory\|author=Paulo Ribenboim\|publisher=Springer\|year=2000\|isbn=978-0-387-98911-2\|page=66}} \| $C_{\mathrm{Artin}}$ \|0.37395 58136 19202 28805 {{MathWorld\|ArtinsConstant\|Artin's Constant}}{{OEIS2C\|A005596}} \| $\prod_{p\text{ prime}} \left(1-\frac{1}{p(p-1)}\right)$ \| data-sort-value="1961" \|Before 1961 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Porter's constant{{cite book\|url=https://books.google.com/books?id=QTcCSegK6jQC&q=%22Porter%E2%80%99s+constant%22&pg=PA80\|title=Constructive, Experimental, and Nonlinear Analysis\|author=Michel A. Théra\|publisher=CMS-AMS\|year=2002\|isbn=978-0-8218-2167-1\|page=77}} \| $C$ \|1.46707 80794 33975 47289 {{MathWorld\|PortersConstant\|Porter's Constant}}{{OEIS2C\|A086237}} \| $\frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}$ where γ is the Euler–Mascheroni constant and {{math\|ζ '(2)}} is the derivative of the Riemann zeta function evaluated at s = 2 \|1961 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Lochs constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf\|title=Continued Fraction Transformation\|author=Steven Finch\|publisher=Harvard University\|year=2007\|page=7\|access-date=2015-02-28\|archive-url=https://web.archive.org/web/20160419114446/http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf\|archive-date=2016-04-19\|url-status=dead}} \| $L$ \|0.97027 01143 92033 92574 {{MathWorld\|LochsConstant\|Lochs' Constant}}{{OEIS2C\|A086819}} \| $\frac {6 \ln 2 \ln 10}{ \pi^2}$ \|1964 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
DeVicci's tesseract constant \| \|1.00743 47568 84279 37609 {{OEIS2C\|A243309}} \|The largest cube that can pass through a 4D hypercube. Positive root of $4x^8{-}28x^6{-}7x^4{+}16x^2{+}16=0$ \|1966 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Lieb's square ice constant{{cite book\|url=http://www.theoremoftheday.org/MathPhysics/Lieb/TotDLieb.pdf\|title=Lieb's Square Ice Theorem\|author=Robin Whitty}} \| \|1.53960 07178 39002 03869 {{MathWorld\|LiebsSquareIceConstant\|Liebs Square Ice Constant}}{{OEIS2C\|A118273}} \| $\left(\frac{4}{3}\right)^\frac{3}{2}=\frac{8}{3\sqrt3}$ \|1967 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="0" style="background:#a6ffa7;\|✓ \|data-sort-value="0" style="background:#a6ffa7;\|✓
Niven's constant{{cite book\|url=https://www.ams.org/journals/proc/1969-022-02/S0002-9939-1969-0241373-5/S0002-9939-1969-0241373-5.pdf\|title=Averages of exponents in factoring integers\|author=Ivan Niven}} \| $C$ \|1.70521 11401 05367 76428 {{MathWorld\|NivensConstant\|Niven's Constant}}{{OEIS2C\|A033150}} \| $1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)$ \|1969 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Stephens' constant{{cite book\|url=http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf\|title=Class Number Theory\|author=Steven Finch\|publisher=Harvard University\|year=2005\|page=8\|access-date=2014-04-15\|archive-url=https://web.archive.org/web/20160419150530/http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf\|archive-date=2016-04-19\|url-status=dead}} \| \|0.57595 99688 92945 43964 {{MathWorld\|StephensConstant\|Stephen's Constant}}{{OEIS2C\|A065478}} \| $\prod_{p\text{ prime}} \left(1 - \frac{p}{p^3-1}\right)$ \|1969 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Regular paperfolding sequence{{cite book\|url=http://carma.newcastle.edu.au/jon/tools1.pdf\|title=Tools for visualizing real numbers.\|author1=Francisco J. Aragón Artacho\|author2=David H. Baileyy\|author3=Jonathan M. Borweinz\|author4=Peter B. Borwein\|year=2012\|page=33\|access-date=2014-01-20\|archive-date=2017-02-20\|archive-url=https://web.archive.org/web/20170220175429/https://carma.newcastle.edu.au/jon/tools1.pdf\|url-status=dead}}{{cite book\|url=http://www.jgiesen.de/Divers/PapierFalten/PapierFalten.pdf\|title=Papierfalten\|year=1998}} \| $P$ \|0.85073 61882 01867 26036 {{refn\|group=Mw\|name=Paper Folding Constant\|{{MathWorld\|PaperFoldingConstant\|Paper Folding Constant}}}}{{OEIS2C\|A143347}} \| $\sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} = \sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}}$ \|1970 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|?
Reciprocal Fibonacci constant{{cite book\|url=http://www.numericana.com/answer/constants.htm#prevost\|title=Numerical Constants\|author=Gérard P. Michon\|publisher=Numericana\|year=2005}} \| $\psi$ \|3.35988 56662 43177 55317 {{MathWorld\|ReciprocalFibonacciConstant\|Reciprocal Fibonacci Constant}}{{OEIS2C\|A079586}} \| $\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots$ where F_n is the n^th Fibonacci number \|1974 \|data-sort-value="2" style="background:#ffa6a6;\|✗ \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Chvátal–Sankoff constant for the binary alphabet \| $\gamma_2$ \| data-sort-value="0.78807" 10000 \| $0.788071 \le \gamma_2 \le 0.826280$ \| $\lim_{n\to\infty}\frac{\operatorname{E}[\lambda_{n,2}]}{n}$ where {{math\|E[λ_n,2]}} is the expected longest common subsequence of two random length-n binary strings \|1975 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Feigenbaum constant δ{{cite book\|url=https://books.google.com/books?id=i633SeDqq-oC&q=669201609&pg=PA500\|title=Chaos: An Introduction to Dynamical Systems\|author=Kathleen T. Alligood\|publisher=Springer\|year=1996\|isbn=978-0-387-94677-1}} \| $\delta$ \|4.66920 16091 02990 67185 {{refn\|group=Mw\|name=Feigenbaum Constant\|{{MathWorld\|FeigenbaumConstant\|Feigenbaum Constant}}}}{{OEIS2C\|A006890}} \| $\lim_{n \to \infty}\frac {a_{n+1}-a_n}{a_{n+2}-a_{n+1}}$ where the sequence a_n is given by n-th period-doubling bifurcation of logistic map $x_{k+1} = a x_k(1-x_k)$ or any other one-dimensional map with a single quadratic maximum \|1975 \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|? \|data-sort-value="1" style="background:#fcffa6;\|?
Chaitin's constants{{cite book\|url=https://books.google.com/books?id=HrOxRdtYYaMC&q=%22Chaitin+constant%22&pg=PA63\|title=The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes\|author=David Darling\|publisher=Wiley & Sons inc.\|year=2004\|isbn=978-0-471-27047-8\|page=63}} \| $\Omega$ \| data-sort-value="0.00787" 49969 97812 3844 \|In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844. {{MathWorld\|ChaitinsConstant\|Chaitin's Constant}}{{OEIS2C\|A100264}} \| $\sum_{p \in P} 2^{-\|p$

class="wikitable sortable sticky-header sort-under"

rowspan="2" | Name

! rowspan="2" | Symbol

! rowspan="2" | Decimal expansion

! rowspan="2" | Formula

! rowspan="2" | Year

! colspan="3" | Set

\mathbb{Q}

! $\mathbb{A}$

! $\mathcal{P}$

One

|Multiplicative identity of $\mathbb{C}$ .

| data-sort-value="-2000" |Prehistory

|data-sort-value="0" style="background:#a6ffa7;|✓

Two

| data-sort-value="-2000" |Prehistory

|data-sort-value="0" style="background:#a6ffa7;|✓

One half

|{{sfrac|1|2}}

| data-sort-value="0.50000" |0.5

| data-sort-value="-2000" |Prehistory

|data-sort-value="0" style="background:#a6ffa7;|✓

| $\pi$

|3.14159 26535 89793 23846 {{MathWorld|PiFormulas|Pi Formulas}}{{OEIS2C|A000796}}

|Ratio of a circle's circumference to its diameter.

| data-sort-value="-1900" |1900 to 1600 BCE {{harvnb|Arndt|Haenel|2006|p=167}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Tau

| $\tau$

|6.28318 53071 79586 47692{{cite web |last1=Hartl |first1=Michael |title=100,000 digits of Tau |url=https://tauday.com/tau-digits |website=Tau Day |access-date=22 January 2023}}{{OEIS2C|A019692}}

|Ratio of a circle's circumference to its radius. Equal to $2\pi$

| data-sort-value="-1900" |1900 to 1600 BCE {{harvnb|Arndt|Haenel|2006|p=167}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Square root of 2,

Pythagoras constant{{cite book|title=Mathematical sorcery: revealing the secrets of numbers|author=Calvin C Clawson|year=2001|isbn=978 0 7382 0496-3|page=IV|publisher=Basic Books}}

| $\sqrt{2}$

|1.41421 35623 73095 04880 {{MathWorld|PythagorassConstant|Pythagoras's Constant}}{{OEIS2C|A002193}}

|Positive root of $x^2=2$

| data-sort-value="-1800" |1800 to 1600 BCEFowler and Robson, p. 368.

[http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection] {{webarchive|url=https://web.archive.org/web/20120813054036/http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html|date=2012-08-13}}

[http://www.math.ubc.ca/%7Ecass/Euclid/ybc/ybc.html High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection]

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Square root of 3,

Theodorus' constant{{cite book|url=https://books.google.com/books?id=xAwukpHCqH0C&q=1.732050807&pg=PA15|title=Figuring Out Mathematics|author=Vijaya AV|publisher=Dorling Kindcrsley (India) Pvt. Lid.|year=2007|isbn=978-81-317-0359-5|page=15}}

| $\sqrt{3}$

|1.73205 08075 68877 29352 {{MathWorld|TheodorussConstant|Theodorus's Constant}}{{OEIS2C|A002194}}

|Positive root of $x^2=3$

| data-sort-value="-465" |465 to 398 BCE

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Square root of 5{{cite book|url=https://books.google.com/books?id=KjMVx6ljh6YC&q=2.236067977&pg=PA24|title=Essential Mathematics 9|author=P A J Lewis|publisher=Ratna Sagar|year=2008|isbn=9788183323673|page=24}}

| $\sqrt{5}$

|2.23606 79774 99789 69640 {{OEIS2C|A002163}}

|Positive root of $x^2=5$

| data-sort-value="-464" |

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Phi, Golden ratio{{cite book|url=https://books.google.com/books?id=ZOfUsvemJDMC&q=1.618033988749894848&pg=PA316|title=The Princeton Companion to Mathematics|author1=Timothy Gowers|author2=June Barrow-Green|author3=Imre Leade|publisher=Princeton University Press|year=2007|isbn=978-0-691-11880-2|page=316}}

| $\varphi$ or $\phi$

|1.61803 39887 49894 84820 {{MathWorld|GoldenRatio|Golden Ratio}}{{OEIS2C|A001622}}

| $\frac{1+\sqrt{5}}{2}$

| data-sort-value="-301" |~300 BCE

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Silver ratio{{citation|last=Kapusta|first=Janos|title=The square, the circle, and the golden proportion: a new class of geometrical constructions|journal=Forma|volume=19|year=2004|pages=293–313|url=http://www.scipress.org/journals/forma/pdf/1904/19040293.pdf|access-date=2022-01-28|archive-date=2020-09-18|archive-url=https://web.archive.org/web/20200918165840/http://www.scipress.org/journals/forma/pdf/1904/19040293.pdf|url-status=dead}}.

| $\delta_S$

|2.41421 35623 73095 04880 {{MathWorld|SilverRatio|Silver Ratio}}{{OEIS2C|A014176}}

| $\sqrt{2}+1$

| data-sort-value="-301" |~300 BCE

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Zero

|Additive identity of $\mathbb{C}$ .

| data-sort-value="-300" |300 to 100 BCEKim Plofker (2009), Mathematics in India, Princeton University Press, {{ISBN|978-0-691-12067-6}}, pp. 54–56.

|data-sort-value="0" style="background:#a6ffa7;|✓

Negative one

| −1

| data-sort-value="-300" |300 to 200 BCE

|data-sort-value="0" style="background:#a6ffa7;|✓

Cube root of 2

| $\sqrt[3]{2}$

|1.25992 10498 94873 16476 {{MathWorld|DelianConstant|Delian Constant}}{{OEIS2C|A002580}}

|Real root of $x^3=2$

|46 to 120 CE{{cite book|author=Plutarch|title=Quaestiones convivales VIII.ii|url=https://ebooks.adelaide.edu.au/p/plutarch/symposiacs/chapter8.html#section80|section=718ef|quote=And therefore Plato himself dislikes Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations|access-date=2019-05-24|archive-date=2009-11-19|archive-url=https://web.archive.org/web/20091119061142/http://ebooks.adelaide.edu.au/p/plutarch/symposiacs/chapter8.html#section80|url-status=dead}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Cube root of 3

| $\sqrt[3]{3}$

|1.44224 95703 07408 38232 {{OEIS2C|A002581}}

|Real root of $x^3=3$

| data-sort-value="47" |

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Twelfth root of 2{{citation|first=Thomas|last=Christensen|title=The Cambridge History of Western Music Theory|year=2002|page=[https://archive.org/details/cambridgehistory0000unse_t8n5/page/205 205]|publisher=Cambridge University Press |isbn=978-0521686983|url=https://archive.org/details/cambridgehistory0000unse_t8n5/page/205}}

| $\sqrt[12]{2}$

|1.05946 30943 59295 26456 {{OEIS2C|A010774}}

|Real root of $x^{12}=2$

| data-sort-value="47" |

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Supergolden ratio{{cite book |last1=Koshy |first1=Thomas |title=Fibonacci and Lucas Numbers with Applications |date=2017 |publisher=John Wiley & Sons |isbn=9781118742174 |edition=2 |url=https://books.google.com/books?id=kAhCDwAAQBAJ&dq=supergolden+ratio%7Cnumber%7Cconstant&pg=PT523 |accessdate=14 August 2018 |language=en}}

| $\psi$

|1.46557 12318 76768 02665 {{OEIS2C|A092526}}

| $\frac{1 + \sqrt[3]{\frac{29 + 3\sqrt{93}}{2}} + \sqrt[3]{\frac{29 - 3\sqrt{93}}{2}}}{3}$

Real root of $x^{3} = x^{2} + 1$

| data-sort-value="47" |

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Imaginary unit{{cite book|url=https://books.google.com/books?id=IKmMKOtSI50C&q=%22This+leads+to+some+amazing+results.+For+example,+Euler+discovered%22&pg=PA66|title=Mathematics: The New Golden Age|author=Keith J. Devlin|publisher=Columbia University Press|year=1999|isbn=978-0-231-11638-1|page=66}}

| $i$

| data-sort-value="0" |{{math|0 + 1i}}

|Principal root of $x^2=-1$ {{refn|group=nb|Both {{math|i}} and {{math|−i}} are roots of this equation, though neither root is truly "positive" nor more fundamental than the other as they are algebraically equivalent. The distinction between signs of {{math|i}} and {{math|−i}} is in some ways arbitrary, but a useful notational device. See imaginary unit for more information.}}

|1501 to 1576

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Connective constant for the hexagonal lattice{{cite book|url=http://www.labri.fr/perso/bousquet/Exposes/fpsac-saw.pdf|title=Two-dimensional self-avoiding walks|author=Mireille Bousquet-Mélou|publisher=CNRS, LaBRI, Bordeaux, France|author-link=Mireille Bousquet-Mélou}}{{cite book|url=http://www.unige.ch/~smirnov/slides/slides-saw.pdf|title=The connective constant of the honeycomb lattice √ (2 + √ 2)|author1=Hugo Duminil-Copin|author2=Stanislav Smirnov|publisher=Université de Geneve|year=2011|name-list-style=amp}}

| $\mu$

|1.84775 90650 22573 51225 {{MathWorld|Self-AvoidingWalkConnectiveConstant|Self-Avoiding Walk Connective Constant}}{{OEIS2C|A179260}}

| $\sqrt{2 + \sqrt{2}}$ , as a root of the polynomial $x ^ 4-4 x ^ 2 + 2=0$

|1593

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Kepler–Bouwkamp constant{{cite arXiv|eprint=1301.6293|class=math.MG|author=Richard J. Mathar|title=Circumscribed Regular Polygons|year=2013}}

| $K'$

|0.11494 20448 53296 20070 {{MathWorld|PolygonInscribing|Polygon Inscribing}}{{OEIS2C|A085365}}

| $\prod_{n=3}^\infty \cos\left(\frac{\pi}{n} \right) = \cos\left(\frac{\pi}{3} \right) \cos\left(\frac{\pi}{4} \right) \cos\left(\frac{\pi}{5}\right) ...$

|1596

|data-sort-value="1" style="background:#fcffa6;|?

Wallis's constant

|2.09455 14815 42326 59148 {{MathWorld|WallissConstant|Wallis's Constant}}{{OEIS2C|A007493}}

| $\sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}}$

Real root of $x^{3} - 2x - 5 = 0$

|1616 to 1703

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Euler's number{{cite book|url=https://books.google.com/books?id=zdBHMHV3m5YC&q=2.7182818284590452353602874&pg=PA76|title=Mathematics and the Imagination|author=E.Kasner y J.Newman.|publisher=Conaculta|year=2007|isbn=978-968-5374-20-0|page=77}}

| $e$

|2.71828 18284 59045 23536 {{MathWorld|e|e}}{{OEIS2C|A001113}}

| $\lim_{n \to \infty} \left( 1 + \frac {1}{n}\right)^n = \sum_{n=0}^{\infty}\frac{1}{n!} = 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} \cdots$

|1618{{cite web|url=http://www-history.mcs.st-and.ac.uk/HistTopics/e.html|title=The number e|last1=O'Connor|first1=J J|last2=Robertson|first2=E F|publisher=MacTutor History of Mathematics}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Natural logarithm of 2{{cite book|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=0.6931471805599&pg=PA182|title=Handbook of Continued Fractions for Special Functions|author1=Annie Cuyt|author1-link= Annie Cuyt |author2=Vigdis Brevik Petersen|author3=Brigitte Verdonk|author4=Haakon Waadeland|author5=William B. Jones|publisher=Springer|year=2008|isbn=978-1-4020-6948-2|page=182}}

| $\ln 2$

|0.69314 71805 59945 30941 {{MathWorld|NaturalLogarithmof2|Natural Logarithm of 2}}{{OEIS2C|A002162}}

|Real root of $e^{x} = 2$

$\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}
= \frac{1}{1} - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots$

|1619{{cite book|url=https://books.google.com/books?id=mGJRjIC9fZgC|title=A History of Mathematics|author-last=Cajori|author-first=Florian|date=1991|publisher=AMS Bookstore|isbn=0-8218-2102-4|edition=5th|page=152|author-link=Florian Cajori}} & 1668 {{cite web|url=http://www-history.mcs.st-and.ac.uk/HistTopics/e.html|title=The number e|author-last1=O'Connor|author-first1=J. J.|date=September 2001|publisher=The MacTutor History of Mathematics archive|access-date=2009-02-02|author-first2=E. F.|author-last2=Robertson}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Lemniscate constant{{cite book|url=https://books.google.com/books?id=aKQhpm1h770C&q=2.6220575&pg=PA333|title=L-Functions and Arithmetic|author1=J. Coates|author2=Martin J. Taylor|publisher=Cambridge University Press|year=1991|isbn=978-0-521-38619-7|page=333}}

| $\varpi$

|2.62205 75542 92119 81046 {{MathWorld|LemniscateConstant|Lemniscate Constant}}{{OEIS2C|A062539}}

| $2\int_{0}^1\frac{dt}{\sqrt{1-t^4}} = \frac14 \sqrt{\frac{2}{\pi}}\,\Gamma {\left(\frac14 \right)^2}$

Ratio of the perimeter of Bernoulli's lemniscate to its diameter.

|1718 to 1798

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Euler's constant

| $\gamma$

|0.57721 56649 01532 86060 {{MathWorld|Euler-MascheroniConstant|Euler–Mascheroni Constant}}{{OEIS2C|A001620}}

| $\lim_{n\to\infty}\left(-\log n + \sum_{k=1}^n \frac1{k}\right)=\int_1^\infty\left(-\frac1x+\frac1{\lfloor x\rfloor}\right)\,dx$

Limiting difference between the harmonic series and the natural logarithm.

|1735

|data-sort-value="1" style="background:#fcffa6;|?

Erdős–Borwein constant{{cite arXiv|eprint=0806.4410|class=math.CA|author=Robert Baillie|title=Summing The Curious Series of Kempner and Irwin|year=2013}}

| $E$

|1.60669 51524 15291 76378 {{MathWorld|Erdos-BorweinConstant|Erdos-Borwein Constant}}{{OEIS2C|A065442}}

| $\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} \! + \! \frac{1}{3} \! + \! \frac{1}{7} \! + \! \frac{1}{15} \! + \! \cdots$

|1749{{cite book|url=http://www.math.dartmouth.edu/~euler/pages/E190.html|title=Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae|author=Leonhard Euler|year=1749|page=108}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Omega constant

| $\Omega$

|0.56714 32904 09783 87299 {{MathWorld|OmegaConstant|Omega Constant}}{{OEIS2C|A030178}}

| $W(1)=\frac{1}{\pi}\int_0^\pi\log\left(1+\frac{\sin t}{t}e^{t\cot t}\right)dt$

where W is the Lambert W function

|1758 & 1783

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Apéry's constant{{cite book|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=1.202056903159594285399738&pg=PA188|title=Handbook of Continued Fractions for Special Functions|author1=Annie Cuyt|author2=Vigdis Brevik Petersen|author3=Brigitte Verdonk|author4=Haakon Waadelantl|author5=William B. Jones.|publisher=Springer|year=2008|isbn=978-1-4020-6948-2|page=188}}

| $\zeta(3)$

|1.20205 69031 59594 28539 {{MathWorld|AperysConstant|Apéry's Constant}}{{OEIS2C|A002117}}

| $\zeta(3)=\sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots$

with the Riemann zeta function $\zeta(s)$ .

|1780

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|data-sort-value="0" style="background:#a6ffa7;|✓

Laplace limit{{cite book|title=Orbital Mechanics for Engineering Students|title-link=Orbital Mechanics for Engineering Students|author=Howard Curtis|publisher=Elsevier|year=2014|isbn=978-0-08-097747-8|page=159}}

|0.66274 34193 49181 58097 {{MathWorld|LaplaceLimit|Laplace Limit}}{{OEIS2C|A033259}}

|Real root of $\frac{ x e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1$

| data-sort-value="1782" |~1782

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Soldner constant{{cite book|url=https://archive.org/details/bub_gb_g4Q_AAAAcAAJ|title=Théorie et tables d'une nouvelle fonction transcendante|author=Johann Georg Soldner|publisher=J. Lindauer, München|year=1809|page=[https://archive.org/details/bub_gb_g4Q_AAAAcAAJ/page/n39 42]|language=fr}}{{cite book|url=https://archive.org/details/bub_gb_XkgDAAAAQAAJ|title=Adnotationes ad calculum integralem Euleri|author=Lorenzo Mascheroni|publisher=Petrus Galeatius, Ticini|year=1792|page=[https://archive.org/details/bub_gb_XkgDAAAAQAAJ/page/n34 17]|language=la}}

| $\mu$

|1.45136 92348 83381 05028 {{MathWorld|SoldnersConstant|Soldner's Constant}}{{OEIS2C|A070769}}

| $\mathrm{li}(x) = \int_0^x \frac{dt}{\ln t} = 0$ ; root of the logarithmic integral function.

|1792

|data-sort-value="1" style="background:#fcffa6;|?

Gauss's constant{{cite book|url=https://books.google.com/books?id=UrSnNeJW10YC&q=%22Gauss%27s+constant%22&pg=PA647|title=An Atlas of Functions: With Equator, the Atlas Function Calculator|author1=Keith B. Oldham|author2=Jan C. Myland|author3=Jerome Spanier|publisher=Springer|year=2009|isbn=978-0-387-48806-6|page=15}}

| $G$

|0.83462 68416 74073 18628 {{MathWorld|GausssConstant|Gauss's Constant}}{{OEIS2C|A014549}}

| $\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{1}{4\pi} \sqrt{\frac{2}{\pi}}\Gamma\left(\frac{1}{4}\right)^2=\frac \varpi\pi$

where agm is the arithmetic–geometric mean and $\varpi$ is the lemniscate constant.

|1799{{Cite book|title=Undergraduate convexity : problems and solutions|last=Nielsen, Mikkel Slot.|date = July 2016|isbn=9789813146211|pages=162|publisher=World Scientific |oclc=951172848}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Second Hermite constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|title=Errata and Addenda to Mathematical Constants|author=Steven Finch|publisher=Harvard.edu|year=2014|access-date=2013-12-17|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|archive-date=2016-03-16|url-status=dead}}

| $\gamma_{2}$

|1.15470 05383 79251 52901 {{MathWorld|HermiteConstants|Hermite Constants}}{{OEIS2C|A246724}}

| $\frac{2}{\sqrt{3}}$

|1822 to 1901

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Liouville's constant{{cite book|title=Mathematical Traveler: Exploring the Grand History of Numbers|author=Calvin C. Clawson|publisher=Perseus|year=2003|isbn=978-0-7382-0835-0|page=187}}

| $L$

|0.11000 10000 00000 00000 0001 {{MathWorld|LiouvillesConstant|Liouville's Constant}}{{OEIS2C|A012245}}

| $\sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}} + \cdots$

| data-sort-value="1844" |Before 1844

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

First continued fraction constant

| $C_1$

|0.69777 46579 64007 98201 {{MathWorld|ContinuedFractionConstants|Continued Fraction Constants}}{{OEIS2C|A052119}}

| $C_1=[0;1,2,3,4,5,...]=\frac{I_1(2)}{I_0(2)}$ , (see Bessel functions). $C_1\notin \mathbb A.$ {{Cite web |last=Waldschmidt |first=Michel |date=2021 |title=Irrationality and transcendence of values of special functions. |url=https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/ValuesSpecialFunctions.pdf}}

|1855{{cite journal |last1=Amoretti |first1=F. |title=Sur la fraction continue [0,1,2,3,4,...] |journal=Nouvelles annales de mathématiques |date=1855 |volume=1 |issue=14 |pages=40–44 |url=http://www.numdam.org/item/?id=NAM_1855_1_14__40_1}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Ramanujan's constant{{cite book|url=https://books.google.com/books?id=txPhITLO1YoC&q=262537412640768743.99999999999925&pg=PA107|title=Modular Forms: A Classical and Computational Introduction|author=L. J. Lloyd James Peter Kilford|publisher=Imperial College Press|year=2008|isbn=978-1-84816-213-6|page=107}}

|262 53741 26407 68743
.99999 99999 99250 073 {{MathWorld|RamanujanConstant|Ramanujan Constant}}{{OEIS2C|A060295}}

| $e^{\pi\sqrt{163}}$

|1859

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Glaisher–Kinkelin constant

| $A$

|1.28242 71291 00622 63687 {{MathWorld|Glaisher-KinkelinConstant|Glaisher-Kinkelin Constant}}{{OEIS2C|A074962}}

| $e^{\frac{1}{12}-\zeta^\prime(-1)} =
e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^\infty \frac{1}{n+1} \sum\limits_{k=0}^n \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)}$

|1860

|data-sort-value="1" style="background:#fcffa6;|?

Catalan's constant{{cite book|url=https://books.google.com/books?id=5Lp-tGZR25sC&q=0.91596559417721901505460351493238411&pg=PA127|title=Number Theory: Volume II: Analytic and Modern Tools|author=Henri Cohen|publisher=Springer|year=2000|isbn=978-0-387-49893-5|page=127}}{{cite book|url=https://books.google.com/books?id=NBcSzUlaWWAC&q=0.915965594177219015&pg=PA29|title=Series Associated With the Zeta and Related Functions|author1=H. M. Srivastava|author2=Choi Junesang|publisher=Kluwer Academic Publishers|year=2001|isbn=978-0-7923-7054-3|page=30}}{{cite book|url=https://books.google.com/books?id=LXZFAAAAcAAJ&pg=PA618|title=Mémoire sur la transformation des séries, et sur quelques intégrales définies, Comptes rendus hebdomadaires des séances de l'Académie des sciences 59|author=E. Catalan|publisher=Kluwer Academic éditeurs|year=1864|page=618}}

| $G$

|0.91596 55941 77219 01505 {{MathWorld|CatalansConstant|Catalan's Constant}}{{OEIS2C|A006752}}

| $\beta(2)=\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^2} = \frac{1}{1^2}-\frac{1}{3^2} + \frac{1}{5^2} - \frac{1}{7^2} + \frac{1}{9^2} + \cdots$

with the Dirichlet beta function $\beta(s)$ .

|1864

|data-sort-value="1" style="background:#fcffa6;|?

|data-sort-value="0" style="background:#a6ffa7;|✓

Dottie number{{cite book|url=https://books.google.com/books?id=eztUxtCfNXoC&q=Single%20Variable%20Calculus%3A%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&pg=PA314|title=Single Variable Calculus: Concepts and Contexts|author=James Stewart|publisher=Brooks/Cole|year=2010|isbn=978-0-495-55972-6|page=314}}

|0.73908 51332 15160 64165 {{MathWorld|DottieNumber|Dottie Number}}{{OEIS2C|A003957}}

|Real root of $\cos x = x$

|1865

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Meissel–Mertens constant{{cite book|url=https://books.google.com/books?id=7-sDtIy8MNIC&q=Khinchin%27s+constant&pg=PA161|title=Gamma: Exploring Euler's Constant|author=Julian Havil|publisher=Princeton University Press|year=2003|isbn=9780691141336|page=64}}

| $M$

|0.26149 72128 47642 78375 {{MathWorld|MertensConstant|Mertens Constant}}{{OEIS2C|A077761}}

| $\lim_{n\to\infty}\left(\sum_{p\le n}\frac{1}{p}-\ln\ln n\right) = \gamma + \sum_{p}\left(\ln\left(1 - \frac{1}{p}\right) + \frac{1}{p}\right)$

where γ is the Euler–Mascheroni constant and p is prime

|1866 & 1873

|data-sort-value="1" style="background:#fcffa6;|?

Universal parabolic constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|title=Errata and Addenda to Mathematical Constants|author=Steven Finch|publisher=Harvard.edu|year=2014|page=59|access-date=2013-12-17|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|archive-date=2016-03-16|url-status=dead}}

| $P$

|2.29558 71493 92638 07403 {{MathWorld|UniversalParabolicConstant|Universal Parabolic Constant}}{{OEIS2C|A103710}}

| $\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arsinh}(1)+\sqrt{2}$

| data-sort-value="1891" |Before 1891{{Cite book|url=https://archive.org/details/anelementarytre00osbogoog|title=An Elementary Treatise on the Differential and Integral Calculus|last=Osborne|first=George Abbott|publisher=Leach, Shewell, and Sanborn|year=1891|pages=[https://archive.org/details/anelementarytre00osbogoog/page/n265 250]}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Cahen's constant{{cite book|url=https://books.google.com/books?id=iAg8FL5jKSgC&q=%22cahen+constant%22&pg=PA72|title=Series representations for some mathematical constants|author=Yann Bugeaud|year=2004|isbn=978-0-521-82329-6|page=72|publisher=Cambridge University Press }}

| $C$

|0.64341 05462 88338 02618 {{MathWorld|CahensConstant|Cahen's Constant}}{{OEIS2C|A118227}}

| $\sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}$

where s_k is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...

|1891

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Gelfond's constant{{cite book|url=https://books.google.com/books?id=7L7xcjBPemEC&q=23.14069&pg=RA2-PA4|title=The Penguin Dictionary of Curious and Interesting Numbers|author=David Wells|author-link=David G. Wells|publisher=Penguin Books Ltd.|year=1997|isbn=9780141929408|page=4}}

| $e^{\pi}$

|23.14069 26327 79269 0057 {{MathWorld|GelfondsConstant|Gelfonds Constant}}{{OEIS2C|A039661}}

| $(-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = 1 + \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2} + \frac{\pi^{3}}{6} + \cdots$

|1900{{cite book|title=Mathematical Developments Arising from Hilbert Problems|last=Tijdeman|first=Robert|publisher=American Mathematical Society|year=1976|isbn=0-8218-1428-1|editor=Felix E. Browder|editor-link=Felix Browder|series=Proceedings of Symposia in Pure Mathematics|volume=XXVIII.1|pages=241–268|chapter=On the Gel'fond–Baker method and its applications|zbl=0341.10026|author-link=Robert Tijdeman}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Gelfond–Schneider constant{{cite book|url=https://books.google.com/books?id=RSU8AAAAQBAJ&q=2.6651&pg=PA328|title=Precalculus: With Unit Circle Trigonometry|author=David Cohen|publisher=Thomson Learning Inc.|year=2006|isbn=978-0-534-40230-3|page=328}}

| $2^{\sqrt{2}}$

|2.66514 41426 90225 18865 {{MathWorld|Gelfond-SchneiderConstant|Gelfond-Schneider Constant}}{{OEIS2C|A007507}}

| $2^{\sqrt{2}}$

| data-sort-value="1902" |Before 1902

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Second Favard constant{{cite book|url=https://books.google.com/books?id=nbjOnJlJfFYC&q=Favard+Constant&pg=PA274|title=Quadrature Theory: The Theory of Numerical Integration on a Compact Interval|author1=Helmut Brass|author2=Knut Petras|publisher=AMS|year=2010|isbn=978-0-8218-5361-0|page=274}}

| $K_{2}$

|1.23370 05501 36169 82735 {{MathWorld|FavardConstants|Favard Constants}}{{OEIS2C|A111003}}

| $\frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n+1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots$

|1902 to 1965

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Golden angle{{cite book|url=http://fibonacci.ucoz.com/index/ang/0-9|title=Ángulo áureo}}

| $g$

|2.39996 32297 28653 32223 {{MathWorld|GoldenAngle|Golden Angle}}{{OEIS2C|A131988}}

| $\frac{2\pi}{\varphi^2} = \pi (3-\sqrt{5})$ or

$180 (3-\sqrt{5})=137.50776\ldots$ in degrees

|1907

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Sierpiński's constant{{cite book|url=https://books.google.com/books?id=aFDWuZZslUUC&q=1.584962500&pg=PA2685|title=CRC Concise Encyclopedia of Mathematics, Second Edition|author=Eric W. Weisstein|publisher=CRC Press|year=2002|isbn=9781420035223|page=1356}}

| $K$

|2.58498 17595 79253 21706 {{MathWorld|SierpinskiConstant|Sierpinski Constant}}{{OEIS2C|A062089}}

| $\begin{align}
&\pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) =
\pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi) \\
&= \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right)
\end{align}$

|1907

|data-sort-value="1" style="background:#fcffa6;|?

Landau–Ramanujan constant{{cite book|url=https://books.google.com/books?id=ZXjHKPS1LEAC&q=Landau-Ramanujan+constant&pg=PA80|title=Prime Numbers: A Computational Perspective|author1=Richard E. Crandall|author2=Carl B. Pomerance|publisher=Springer|year=2005|isbn=978-0387-25282-7|page=80}}

| $K$

|0.76422 36535 89220 66299 {{MathWorld|Landau-RamanujanConstant|Landau-Ramanujan Constant}}{{OEIS2C|A064533}}

| $\frac1{\sqrt2}\prod_{{p \equiv 3 \text{ mod } 4}\atop p \;{\rm prime}} {\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{{p \equiv 1 \text{ mod } 4}\atop p \;{\rm prime}} {\left(1-\frac1{p^2}\right)^\frac{1}{2}}$

|1908

|data-sort-value="1" style="background:#fcffa6;|?

First Nielsen–Ramanujan constant{{cite book|url=http://bitman.name/math/article/872|title=Nielsen – Ramanujan (costanti di)|author=Mauro Fiorentini}}

| $a_{1}$

|0.82246 70334 24113 21823 {{MathWorld|Nielsen-RamanujanConstants|Nielsen-Ramanujan Constants}}{{OEIS2C|A072691}}

| $\frac{{\zeta}(2)}{2} = \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} {-} \frac{1}{2^2} {+} \frac{1}{3^2} {-} \frac{1}{4^2} {+} \cdots$

|1909

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Gieseking constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf|title=Volumes of Hyperbolic 3-Manifolds|author=Steven Finch|publisher=Harvard University|archive-url=https://web.archive.org/web/20150919160427/http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf|archive-date=2015-09-19|url-status=dead}}

| $G$

|1.01494 16064 09653 62502 {{MathWorld|GiesekingsConstant|Gieseking's Constant}}{{OEIS2C|A143298}}

| $\frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)$
$=\frac{\sqrt 3}{3}\left(\frac{\psi_1(1/3)}{2}-\frac{\pi^2}{3}\right)$ with the trigamma function $\psi_1$ .

|1912

|data-sort-value="1" style="background:#fcffa6;|?

|data-sort-value="0" style="background:#a6ffa7;|✓

Bernstein's constant{{cite book|url=https://books.google.com/books?id=En41UGQ6YXsC&q=0.28016949902386913303643649&pg=PA211|title=Approximation Theory and Approximation Practice|author=Lloyd N. Trefethen|publisher=SIAM|year=2013|isbn=978-1-611972-39-9|page=211}}

| $\beta$

|0.28016 94990 23869 13303 {{MathWorld|BernsteinsConstant|Bernstein's Constant}}{{OEIS2C|A073001}}

| $\lim_{n\to\infty} 2n E_{2n}(f)$ , where E_n(f) is the error of the best uniform approximation to a real function f(x) on the interval [−1, 1] by real polynomials of no more than degree n, and f(x) = |x|

|1913

|data-sort-value="1" style="background:#fcffa6;|?

Tribonacci constant{{Cite journal |last=Agronomof |first=M. |year=1914 |title=Sur une suite récurrente. |journal=Mathesis |volume=4 |pages=125–126}}

|1.83928 67552 14161 13255 {{MathWorld|TribonacciConstant|Tribonacci Constant}}{{OEIS2C|A058265}}

| $\frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3} = \frac{1+4\cosh\left(\frac{1}{3}\cosh^{-1}\left(2+\frac{3}{8}\right)\right)}{3}$

Real root of $x^{3} - x^{2} - x - 1 = 0$

|1914 to 1963

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Brun's constant{{Cite book |last=Thomas Koshy |url=https://books.google.com/books?id=d5Z5I3gnFh0C&q=Brun+constant&pg=PA118 |title=Elementary Number Theory with Applications |publisher=Elsevier |year=2007 |isbn=978-0-12-372-487-8 |page=119}}

| $B_{2}$

|1.90216 05831 04 {{refn|group=Mw|name=Brun's Constant|{{MathWorld|BrunsConstant|Brun's Constant}}}}{{OEIS2C|A065421}}

| $\textstyle {\sum\limits_p(\frac1{p}+\frac1{p+2})} = (\frac1{3} \! + \! \frac1{5}) + (\tfrac1{5} \! + \! \tfrac1{7}) + (\tfrac1{11} \! + \! \tfrac1{13}) + \cdots$

where the sum ranges over all primes p such that p + 2 is also a prime

|1919

|data-sort-value="1" style="background:#fcffa6;|?

Twin primes constant

| $C_{2}$

|0.66016 18158 46869 57392 {{MathWorld|TwinPrimesConstant|Twin Primes Constant}}{{OEIS2C|A005597}}

| $\prod_{\textstyle{p\;{\rm prime}\atop p \ge 3}} \left(1 - \frac{1}{(p-1)^2}\right)$

|1922

|data-sort-value="1" style="background:#fcffa6;|?

Plastic ratio{{cite book|url=https://books.google.com/books?id=oW6Xeo8EmDgC&q=%22Plastic+number%22&pg=PT120|title=Professor Stewart's Cabinet of Mathematical Curiosities|author=Ian Stewart|publisher=Birkhäuser Verlag|year=1996|isbn=978-1-84765-128-0}}

| $\rho$

|1.32471 79572 44746 02596 {{MathWorld|PlasticConstant|Plastic Constant}}{{OEIS2C|A060006}}

| $\sqrt[3]{1 + \! \sqrt[3]{1 + \! \sqrt[3]{1 + \cdots}}} = \textstyle \sqrt[3]{\frac{1}{2}+\frac{\sqrt{69}}{18}}+\sqrt[3]{\frac{1}{2}-\frac{\sqrt{69}}{18}}$

Real root of $x^{3} = x + 1$

|1924

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Bloch's constant{{cite book|url=https://books.google.com/books?id=aFDWuZZslUUC&q=Bloch-Landau+constant&pg=PA1688|title=CRC Concise Encyclopedia of Mathematics, Second Edition|author=Eric W. Weisstein|publisher=CRC Press|year=2003|isbn=978-1-58488-347-0|page=1688}}

| $B$

| data-sort-value="0.43320" | $0.4332\leq B\leq 0.4719$ {{MathWorld|BlochConstant|Bloch Constant}}{{OEIS2C|A085508}}

|The best known bounds are $\frac{\sqrt{3}}{4}+2\times10^{-4}\leq B\leq \sqrt{\frac{\sqrt{3}-1}{2}}\cdot\frac{\Gamma(\frac{1}{3})\Gamma(\frac{11}{12})}{\Gamma(\frac{1}{4})}$

|1925

|data-sort-value="1" style="background:#fcffa6;|?

Z score for the 97.5 percentile point

{{Citation| last=Rees | first=DG |title=Foundations of Statistics| page=246 |publisher=CRC Press |isbn=0-412-28560-6| quote=Why 95% confidence? Why not some other confidence level? The use of 95% is partly convention, but levels such as 90%, 98% and sometimes 99.9% are also used.| year=1987}}{{cite web

|url = http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm

|title = Engineering Statistics Handbook: Confidence Limits for the Mean

|accessdate = 2008-02-04

|publisher = National Institute of Standards and Technology

|quote = Although the choice of confidence coefficient is somewhat arbitrary, in practice 90%, 95%, and 99% intervals are often used, with 95% being the most commonly used.

|archiveurl = https://web.archive.org/web/20080205120031/http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm

|archivedate = 5 February 2008

|url-status = dead

|df = dmy-all

}}

{{Citation | title=Real-Life Math: Statistics | first1=Eric T | last1=Olson | first2=Tammy Perry | last2=Olson | page=[https://archive.org/details/statistics0000olso/page/66 66] | publisher=Walch Publishing | year=2000 | isbn=0-8251-3863-9 | quote=While other stricter, or looser, limits may be chosen, the 95 percent interval is very often preferred by statisticians. | url=https://archive.org/details/statistics0000olso/page/66 }}{{cite journal|doi=10.1080/03610920802255856|last=Swift| first=MB| title=Comparison of Confidence Intervals for a Poisson Mean – Further Considerations|journal=Communications in Statistics – Theory and Methods|year=2009 | volume=38| issue=5| pages=748–759|s2cid=120748700 | quote=In modern applied practice, almost all confidence intervals are stated at the 95% level.}}

| $z_{.975}$

|1.95996 39845 40054 23552 {{MathWorld|ConfidenceInterval|Confidence Interval}}{{OEIS2C|A220510}}

| $\sqrt{2}\operatorname{erf}^{-1}(0.95)$ where {{math|erf⁻¹(x)}} is the inverse error function

Real number $z$ such that $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{z} e^{-x^2/2} \, \mathrm{d}x = 0.975$

|1925

|data-sort-value="1" style="background:#fcffa6;|?

Landau's constant

| $L$

| data-sort-value="0.50000" | $0.5 < L \le 0.54326$ {{MathWorld|LandauConstant|Landau Constant}}{{OEIS2C|A081760}}

|The best known bounds are $0.5 < L \le \frac{\Gamma(\frac{1}{3})\Gamma(\frac{5}{6})}{\Gamma(\frac{1}{6})}$

|1929

|data-sort-value="1" style="background:#fcffa6;|?

Landau's third constant

| $A$

| data-sort-value="0.50000" | $0.5 < A \le 0.7853$

|1929

|data-sort-value="1" style="background:#fcffa6;|?

Prouhet–Thue–Morse constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|title=Errata and Addenda to Mathematical Constants|author=Steven Finch|publisher=Harvard.edu|year=2014|page=53|access-date=2013-12-17|archive-url=https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf|archive-date=2016-03-16|url-status=dead}}

| $\tau$

|0.41245 40336 40107 59778 {{MathWorld|Thue-MorseConstant|Thue-Morse Constant}}{{OEIS2C|A014571}}

| $\sum_{n=0}^{\infty} \frac{t_n}{2^{n+1}} = \frac{1}{4}\left[2-\prod_{n=0}^{\infty}\left(1-\frac{1}{2^{2^n}}\right)\right]$

where ${t_n}$ is the n^th term of the Thue–Morse sequence

|1929

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Golomb–Dickman constant{{cite book|url=https://books.google.com/books?id=aFDWuZZslUUC&q=Golomb%E2%80%93Dickman+constant&pg=PA1211|title=CRC Concise Encyclopedia of Mathematics|author=Eric W. Weisstein|publisher=Crc Press|year=2002|isbn=9781420035223|page=1212}}

| $\lambda$

|0.62432 99885 43550 87099 {{MathWorld|Golomb-DickmanConstant|Golomb–Dickman Constant}}{{OEIS2C|A084945}}

| $\int_{0}^{1} e^{\mathrm{Li}(t)} dt = \int_0^{\infty} \frac{\rho(t)}{t+2} dt$

where Li(t) is the logarithmic integral, and ρ(t) is the Dickman function

|1930 & 1964

|data-sort-value="1" style="background:#fcffa6;|?

Constant related to the asymptotic behavior of Lebesgue constants{{cite journal|author=Horst Alzer|year=2002|title=Journal of Computational and Applied Mathematics, Volume 139, Issue 2|url=http://ac.els-cdn.com/S0377042701004265/1-s2.0-S0377042701004265-main.pdf?_tid=c20cf466-f4bf-11e3-bd9c-00000aacb362&acdnat=1402859198_57de7868bcc50086f092c66898ec6a33|journal=Journal of Computational and Applied Mathematics|volume=139|issue=2|pages=215–230|doi=10.1016/S0377-0427(01)00426-5|doi-access=free}}

| $c$

|0.98943 12738 31146 95174 {{MathWorld|LebesgueConstants|Lebesgue Constants}}{{OEIS2C|A243277}}

| $\lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=}
\frac{4}{\pi^2}\!\left({-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}{+}{\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}}
\right)$

|1930

|data-sort-value="1" style="background:#fcffa6;|?

Feller–Tornier constant{{cite book|url=https://www.ams.org/journals/tran/1964-112-02/S0002-9947-1964-0166181-5/S0002-9947-1964-0166181-5.pdf|title=SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS|author=ECKFORD COHEN|publisher=University of Tennessee|year=1962|page=220}}

| $\mathcal{C}_{\mathrm{FT}}$

|0.66131 70494 69622 33528 {{MathWorld|Feller-TornierConstant|Feller–Tornier Constant}}{{OEIS2C|A065493}}

| ${\frac{1}{2}\prod_{p\text{ prime}} \left(1-\frac{2}{p^2}\right) + \frac{1}{2}} =\frac{3}{\pi^2}\prod_{p\text{ prime}} \left(1-\frac{1}{p^2-1}\right) + \frac{1}{2}$

|1932

|data-sort-value="1" style="background:#fcffa6;|?

Base 10 Champernowne constant{{cite book|url=https://books.google.com/books?id=wRWyMbmJTMYC&q=%22Champernowne+number%22&pg=PA109|title=Computation, Physics and Beyond|author1=Michael J. Dinneen|author2=Bakhadyr Khoussainov|author3=Prof. Andre Nies|publisher=Springer|year=2012|isbn=978-3-642-27653-8|page=110}}

| $C_{10}$

|0.12345 67891 01112 13141 {{MathWorld|ChampernowneConstant|Champernowne Constant}}{{OEIS2C|A033307}}

|Defined by concatenating representations of successive integers:

0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...

|1933

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Salem constant{{cite book|url=https://books.google.com/books?id=LYT5sBm_Ie0C&q=1.1762808&pg=PA246|title=Distribution Theory of Algebraic Numbers|author=Pei-Chu Hu, Chung-Chun|publisher=Hong Kong University|year=2008|isbn=978-3-11-020536-7|page=246}}

| $\sigma_{10}$

|1.17628 08182 59917 50654 {{MathWorld|SalemConstants|Salem Constants}}{{OEIS2C|A073011}}

|Largest real root of $x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1=0$

|1933

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Khinchin's constant{{cite book|url=https://books.google.com/books?id=7-sDtIy8MNIC&q=Khinchin%27s+constant&pg=PA161|title=Gamma: Exploring Euler's Constant|author=Julian Havil|publisher=Princeton University Press|year=2003|isbn=9780691141336|page=161}}

| $K_{0}$

|{{nobr|2.68545 20010 65306 44530}} {{MathWorld|KhinchinsConstant|Khinchin's Constant}}{{OEIS2C|A002210}}

| $\prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\log_2(n)}$

|1934

|data-sort-value="1" style="background:#fcffa6;|?

Lévy's constant (1){{cite book|url=https://books.google.com/books?id=R7Fp8vytgeAC&pg=PA66|title=Continued Fractions|author=Aleksandr I͡Akovlevich Khinchin|publisher=Courier Dover Publications|year=1997|isbn=978-0-486-69630-0|page=66}}

| $\beta$

|1.18656 91104 15625 45282 {{MathWorld|LevyConstant|Levy Constant}}{{OEIS2C|A100199}}

| $\frac {\pi^2}{12\,\ln 2}$

|1935

|data-sort-value="1" style="background:#fcffa6;|?

Lévy's constant (2){{cite journal|arxiv=1002.4171|author=Marek Wolf|title=Two arguments that the nontrivial zeros of the Riemann zeta function are irrational|journal=Computational Methods in Science and Technology|year=2018|volume=24|issue=4|pages=215–220|doi=10.12921/cmst.2018.0000049|s2cid=115174293}}

| $e^{\beta}$

|3.27582 29187 21811 15978 {{MathWorld|LevyConstant|Levy Constant}}{{OEIS2C|A086702}}

| $e^{\pi^2/(12\ln2)}$

|1936

|data-sort-value="1" style="background:#fcffa6;|?

Copeland–Erdős constant{{cite book|url=https://books.google.com/books?id=NeEpoAf7k0IC&q=0.235711131719232931&pg=PA87|title=Distribution Modulo One and Diophantine Approximation|author=Yann Bugeaud|publisher=Cambridge University Press|year=2012|isbn=978-0-521-11169-0|page=87}}

| $\mathcal{C}_{CE}$

|0.23571 11317 19232 93137 {{MathWorld|Copeland-ErdosConstant|Copeland–Erdos Constant}}{{OEIS2C|A033308}}

|Defined by concatenating representations of successive prime numbers:

0.2 3 5 7 11 13 17 19 23 29 31 37 ...

|1946

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Mills' constant{{cite book|title=Stealth Ciphers|author=Laith Saadi|publisher=Trafford Publishing|year=2004|isbn=978-1-4120-2409-9|page=160}}

| $A$

|1.30637 78838 63080 69046 {{MathWorld|MillsConstant|Mills Constant}}{{OEIS2C|A051021}}

|Smallest positive real number A such that $\lfloor A^{3^{n}} \rfloor$ is prime for all positive integers n

|1947

|data-sort-value="1" style="background:#fcffa6;|?

Gompertz constant{{cite book|url=https://books.google.com/books?id=DQtpJaEs4NIC&q=Gompertz+constant&pg=PA190|title=Handbook of continued fractions for special functions|author1=Annie Cuyt|author2=Viadis Brevik Petersen|author3=Brigitte Verdonk|author4=William B. Jones|publisher=Springer Science|year=2008|isbn=978-1-4020-6948-2|page=190}}

| $\delta$

|0.59634 73623 23194 07434 {{MathWorld|GompertzConstant|Gompertz Constant}}{{OEIS2C|A073003}}

| $\int_0^\infty \!\! \frac{e^{-x}}{1+x} \, dx = \!\! \int_0^1 \!\! \frac{dx}{1-\ln x} = {\tfrac 1 {1+\tfrac 1{1+\tfrac 1{1+\tfrac 2{1+\tfrac 2{1+\tfrac 3{1+3{/\cdots}} }}}}}}$

| data-sort-value="1948" |Before 1948

|data-sort-value="1" style="background:#fcffa6;|?

de Bruijn–Newman constant

| $\Lambda$

| data-sort-value="0" | $0\le\Lambda\le0.2$

|The number Λ such that $H(\lambda,z)=\int^{\infty}_0e^{\lambda u^2}\Phi(u)\cos(zu)du$ has real zeros if and only if λ ≥ Λ.

where $\Phi(u)=\sum_{n=1}^{\infty}(2\pi^2n^4e^{9u}-3\pi n^2e^{5u})e^{-\pi n^2e^{4u}}$ .

|1950

|data-sort-value="1" style="background:#fcffa6;|?

Van der Pauw constant

| $\frac{\pi}{\ln 2}$

|4.53236 01418 27193 80962 {{OEIS2C|A163973}}

| $\frac{\pi}{\ln 2}$

| data-sort-value="1958" |Before 1958 {{OEIS2C|A163973}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Magic angle{{cite book|url=https://books.google.com/books?id=WoaxgpHu19gC&q=0.955316&pg=PA150|title=Discrete Geometry|author=Andras Bezdek|publisher=Marcel Dekkcr, Inc.|year=2003|isbn=978-0-8247-0968-6|page=150}}

| $\theta_{\mathrm{m}}$

|0.95531 66181 245092 78163 {{OEIS2C|A195696}}

| $\arctan \sqrt{2} = \arccos \tfrac{1}{\sqrt 3} \approx \textstyle {54.7356} ^{ \circ }$

| data-sort-value="1959" |Before 1959 {{Cite journal|last=Lowe|first=I. J.|date=1959-04-01|title=Free Induction Decays of Rotating Solids|url=https://link.aps.org/doi/10.1103/PhysRevLett.2.285|journal=Physical Review Letters|language=en|volume=2|issue=7|pages=285–287|doi=10.1103/PhysRevLett.2.285|bibcode=1959PhRvL...2..285L |issn=0031-9007}}

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Artin's constant{{cite book|url=https://books.google.com/books?id=EiYvlcimEi4C&q=1.9287800&pg=PA66|title=My Numbers, My Friends: Popular Lectures on Number Theory|author=Paulo Ribenboim|publisher=Springer|year=2000|isbn=978-0-387-98911-2|page=66}}

| $C_{\mathrm{Artin}}$

|0.37395 58136 19202 28805 {{MathWorld|ArtinsConstant|Artin's Constant}}{{OEIS2C|A005596}}

| $\prod_{p\text{ prime}} \left(1-\frac{1}{p(p-1)}\right)$

| data-sort-value="1961" |Before 1961

|data-sort-value="1" style="background:#fcffa6;|?

Porter's constant{{cite book|url=https://books.google.com/books?id=QTcCSegK6jQC&q=%22Porter%E2%80%99s+constant%22&pg=PA80|title=Constructive, Experimental, and Nonlinear Analysis|author=Michel A. Théra|publisher=CMS-AMS|year=2002|isbn=978-0-8218-2167-1|page=77}}

| $C$

|1.46707 80794 33975 47289 {{MathWorld|PortersConstant|Porter's Constant}}{{OEIS2C|A086237}}

| $\frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}$

where γ is the Euler–Mascheroni constant and {{math|ζ '(2)}} is the derivative of the Riemann zeta function evaluated at s = 2

|1961

|data-sort-value="1" style="background:#fcffa6;|?

Lochs constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf|title=Continued Fraction Transformation|author=Steven Finch|publisher=Harvard University|year=2007|page=7|access-date=2015-02-28|archive-url=https://web.archive.org/web/20160419114446/http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf|archive-date=2016-04-19|url-status=dead}}

| $L$

|0.97027 01143 92033 92574 {{MathWorld|LochsConstant|Lochs' Constant}}{{OEIS2C|A086819}}

| $\frac {6 \ln 2 \ln 10}{ \pi^2}$

|1964

|data-sort-value="1" style="background:#fcffa6;|?

DeVicci's tesseract constant

|1.00743 47568 84279 37609 {{OEIS2C|A243309}}

|The largest cube that can pass through a 4D hypercube.

Positive root of $4x^8{-}28x^6{-}7x^4{+}16x^2{+}16=0$

|1966

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Lieb's square ice constant{{cite book|url=http://www.theoremoftheday.org/MathPhysics/Lieb/TotDLieb.pdf|title=Lieb's Square Ice Theorem|author=Robin Whitty}}

|1.53960 07178 39002 03869 {{MathWorld|LiebsSquareIceConstant|Liebs Square Ice Constant}}{{OEIS2C|A118273}}

| $\left(\frac{4}{3}\right)^\frac{3}{2}=\frac{8}{3\sqrt3}$

|1967

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

Niven's constant{{cite book|url=https://www.ams.org/journals/proc/1969-022-02/S0002-9939-1969-0241373-5/S0002-9939-1969-0241373-5.pdf|title=Averages of exponents in factoring integers|author=Ivan Niven}}

| $C$

|1.70521 11401 05367 76428 {{MathWorld|NivensConstant|Niven's Constant}}{{OEIS2C|A033150}}

| $1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)$

|1969

|data-sort-value="1" style="background:#fcffa6;|?

Stephens' constant{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf|title=Class Number Theory|author=Steven Finch|publisher=Harvard University|year=2005|page=8|access-date=2014-04-15|archive-url=https://web.archive.org/web/20160419150530/http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf|archive-date=2016-04-19|url-status=dead}}

|0.57595 99688 92945 43964 {{MathWorld|StephensConstant|Stephen's Constant}}{{OEIS2C|A065478}}

| $\prod_{p\text{ prime}} \left(1 - \frac{p}{p^3-1}\right)$

|1969

|data-sort-value="1" style="background:#fcffa6;|?

Regular paperfolding sequence{{cite book|url=http://carma.newcastle.edu.au/jon/tools1.pdf|title=Tools for visualizing real numbers.|author1=Francisco J. Aragón Artacho|author2=David H. Baileyy|author3=Jonathan M. Borweinz|author4=Peter B. Borwein|year=2012|page=33|access-date=2014-01-20|archive-date=2017-02-20|archive-url=https://web.archive.org/web/20170220175429/https://carma.newcastle.edu.au/jon/tools1.pdf|url-status=dead}}{{cite book|url=http://www.jgiesen.de/Divers/PapierFalten/PapierFalten.pdf|title=Papierfalten|year=1998}}

| $P$

|0.85073 61882 01867 26036 {{refn|group=Mw|name=Paper Folding Constant|{{MathWorld|PaperFoldingConstant|Paper Folding Constant}}}}{{OEIS2C|A143347}}

| $\sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} =
\sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}}$

|1970

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Reciprocal Fibonacci constant{{cite book|url=http://www.numericana.com/answer/constants.htm#prevost|title=Numerical Constants|author=Gérard P. Michon|publisher=Numericana|year=2005}}

| $\psi$

|3.35988 56662 43177 55317 {{MathWorld|ReciprocalFibonacciConstant|Reciprocal Fibonacci Constant}}{{OEIS2C|A079586}}

| $\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots$

where F_n is the n^th Fibonacci number

|1974

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

Chvátal–Sankoff constant for the binary alphabet

| $\gamma_2$

| data-sort-value="0.78807" 10000 | $0.788071 \le \gamma_2 \le 0.826280$

| $\lim_{n\to\infty}\frac{\operatorname{E}[\lambda_{n,2}]}{n}$

where {{math|E[λ_n,2]}} is the expected longest common subsequence of two random length-n binary strings

|1975

|data-sort-value="1" style="background:#fcffa6;|?

Feigenbaum constant δ{{cite book|url=https://books.google.com/books?id=i633SeDqq-oC&q=669201609&pg=PA500|title=Chaos: An Introduction to Dynamical Systems|author=Kathleen T. Alligood|publisher=Springer|year=1996|isbn=978-0-387-94677-1}}

| $\delta$

|4.66920 16091 02990 67185 {{refn|group=Mw|name=Feigenbaum Constant|{{MathWorld|FeigenbaumConstant|Feigenbaum Constant}}}}{{OEIS2C|A006890}}

| $\lim_{n \to \infty}\frac {a_{n+1}-a_n}{a_{n+2}-a_{n+1}}$

where the sequence a_n is given by n-th period-doubling bifurcation of logistic map $x_{k+1} = a x_k(1-x_k)$ or any other one-dimensional map with a single quadratic maximum

|1975

|data-sort-value="1" style="background:#fcffa6;|?

Chaitin's constants{{cite book|url=https://books.google.com/books?id=HrOxRdtYYaMC&q=%22Chaitin+constant%22&pg=PA63|title=The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes|author=David Darling|publisher=Wiley & Sons inc.|year=2004|isbn=978-0-471-27047-8|page=63}}

| $\Omega$

| data-sort-value="0.00787" 49969 97812 3844 |In general they are uncomputable numbers.
But one such number is 0.00787 49969 97812 3844.
{{MathWorld|ChaitinsConstant|Chaitin's Constant}}{{OEIS2C|A100264}}

| $\sum_{p \in P} 2^{-|p$

{{Mvar|p}}: Halted program
{{math|{{Abs|{{mvar|p}}}}}}: Size in bits of program {{Mvar|p}}
{{Mvar|P}}: Domain of all programs that stop.

|1975

|data-sort-value="2" style="background:#ffa6a6;|✗

|Robbins constant{{cite book|url=https://archive.org/details/mathematicalcons0000finc|url-access=registration|quote=Schmutz.|title=Mathematical Constants|author=Steven R. Finch|publisher=Cambridge University Press|year=2003|isbn=978-3-540-67695-9|page=[https://archive.org/details/mathematicalcons0000finc/page/479 479]}}

| $\Delta(3)$

|0.66170 71822 67176 23515 {{MathWorld|RobbinsConstant|Robbins Constant}}{{OEIS2C|A073012}}

| $\frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5}$

|1977

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

|Weierstrass constant{{cite book|url=https://books.google.com/books?id=aFDWuZZslUUC&q=%22Weierstrass+Constant%22&pg=PA3184|title=CRC Concise Encyclopedia of Mathematics, Second Edition|author=Eric W. Weisstein|publisher=CRC Press|year=2003|isbn=978-1-58488-347-0|page=151}}

|0.47494 93799 87920 65033 {{MathWorld|WeierstrassConstant|Weierstrass Constant}}{{OEIS2C|A094692}}

| $\frac{2^{5/4} \sqrt{\pi} \, e^{\pi/8}}{\Gamma(\frac{1}{4})^{2}}$

| data-sort-value="1978" |Before 1978Waldschmidt, M. "Nombres transcendants et fonctions sigma de Weierstrass." C. R. Math. Rep. Acad. Sci. Canada 1, 111-114, 1978/79.

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|Fransén–Robinson constant{{cite book|url=http://www.advancesindifferenceequations.com/content/pdf/1687-1847-2012-22.pdf|title=Orthogonal and diagonal dimension fluxes of hyperspherical function|author1=Dusko Letic|author2=Nenad Cakic|author3=Branko Davidovic|author4=Ivana Berkovic|publisher=Springer}}

| $F$

|2.80777 02420 28519 36522 {{MathWorld|Fransen-RobinsonConstant|Fransen-Robinson Constant}}{{OEIS2C|A058655}}

| $\int_{0}^\infty \frac{dx}{\Gamma(x)} = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx$

|1978

|data-sort-value="1" style="background:#fcffa6;|?

|Feigenbaum constant α{{cite book|url=https://books.google.com/books?id=DhCbYXzLFLsC&q=2.502907875095892822283902873218&pg=PA7|title=Chaos in Electric Drive Systems: Analysis, Control and Application|author1=K. T. Chau|author2=Zheng Wang|publisher=John Wiley & Son|year=201|isbn=978-0-470-82633-1|page=7}}

| $\alpha$

|2.50290 78750 95892 82228 {{refn|group=Mw|name=Feigenbaum Constant}}{{OEIS2C|A006891}}

|Ratio between the width of a tine and the width of one of its two subtines in a bifurcation diagram

|1979

|data-sort-value="1" style="background:#fcffa6;|?

|Second du Bois-Reymond constant{{cite book|url=https://archive.org/details/mathematicalcons0000finc|url-access=registration|title=Mathematical Constants|author=Steven R. Finch|publisher=Cambridge University Press|year=2003|isbn=978-3-540-67695-9|page=[https://archive.org/details/mathematicalcons0000finc/page/238 238]}}

| $C_2$

|0.19452 80494 65325 11361 {{MathWorld|duBois-ReymondConstants|du Bois-Reymond Constants}}{{OEIS2C|A062546}}

| $\frac{e^2-7}{2} = \int_0^\infty \left|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^2}\right|\,dt-1$

|1983

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|Erdős–Tenenbaum–Ford constant

| $\delta$

|0.08607 13320 55934 20688 {{OEIS2C|A074738}}

| $1-\frac{1+\log\log2}{\log2}$

|1984

|data-sort-value="1" style="background:#fcffa6;|?

|Conway's constant{{cite book|url=https://books.google.com/books?id=gmCSpNhXMooC&q=Conway%20Constant&pg=PA45|title=Mathematics Frontiers|author=Facts On File, Incorporated|year=1997|isbn=978-0-8160-5427-5|page=46|publisher=Infobase }}

| $\lambda$

|1.30357 72690 34296 39125 {{MathWorld|ConwaysConstant|Conway's Constant}}{{OEIS2C|A014715}}

|Real root of the polynomial:

$\begin{smallmatrix}
x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\
-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\
+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\
-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\
-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\
+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\
+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad
\end{smallmatrix}$

|1987

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="0" style="background:#a6ffa7;|✓

|Hafner–Sarnak–McCurley constant{{cite book|url=https://books.google.com/books?id=Pl5I2ZSI6uAC&q=%22Hafner-Sarnak-McCurley+constant%22&pg=PA110|title=Mathematical Constants|author=Steven R. Finch|year=2003|isbn=978-3-540-67695-9|page=110|publisher=Cambridge University Press }}

| $\sigma$

|0.35323 63718 54995 98454 {{MathWorld|Hafner-Sarnak-McCurleyConstant|Hafner-Sarnak-McCurley Constant}}{{OEIS2C|A085849}}

| $\prod_{p\text{ prime}}{\left(1- \left(1-\prod_{n\ge1}\left(1-\frac{1}{p^n}\right)\right)^2 \right)} \!$

|1991

|data-sort-value="1" style="background:#fcffa6;|?

|Backhouse's constant{{cite book|url=https://books.google.com/books?id=aFDWuZZslUUC&q=Backhouse+constant&pg=PA151|title=CRC Concise Encyclopedia of Mathematics, Second Edition|author=Eric W. Weisstein|publisher=CRC Press|year=2003|isbn=978-1-58488-347-0|page=151}}

| $B$

|1.45607 49485 82689 67139 {{MathWorld|BackhousesConstant|Backhouse's Constant}}{{OEIS2C|A072508}}

| $\lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert \quad \scriptstyle \text {where:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k$

$P(x) = 1+\sum_{k=1}^\infty {p_k x^k} = 1+2x+3x^2+5x^3+\cdots$ where p_k is the k^th prime number

|1995

|data-sort-value="1" style="background:#fcffa6;|?

|Viswanath constant{{cite book|url=https://www.ams.org/journals/mcom/2000-69-231/S0025-5718-99-01145-X/S0025-5718-99-01145-X.pdf|title=RANDOM FIBONACCI SEQUENCES AND THE NUMBER 1.13198824...|author=DIVAKAR VISWANATH|publisher=MATHEMATICS OF COMPUTATION|year=1999}}

|1.13198 82487 943 {{MathWorld|RandomFibonacciSequence|Random Fibonacci Sequence}}{{OEIS2C|A078416}}

| $\lim_{n \to \infty}|f_n|^\frac{1}{n}$ where f_n = f_n−1 ± f_n−2, where the signs + or − are chosen at random with equal probability 1/2

|1997

|data-sort-value="1" style="background:#fcffa6;|?

|Komornik–Loreti constant{{cite book|url=http://dmg.tuwien.ac.at/drmota/DiplomarbeitLanz.pdf|title=k-Automatic Reals|author=Christoph Lanz|publisher=Technischen Universität Wien}}

| $q$

|1.78723 16501 82965 93301 {{MathWorld|Komornik-LoretiConstant|Komornik-Loreti Constant}}{{OEIS2C|A055060}}

|Real number $q$ such that $1 = \sum_{k=1}^\infty \frac{t_k}{q^k}$ , or $\prod_{n=0}^\infty\left (1-\frac{1}{q^{2^n}}\right )+\frac{q-2}{q-1}=0$

where t_k is the k^th term of the Thue–Morse sequence

|1998

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|Embree–Trefethen constant

| $\beta^{\star}$

|0.70258

|1999

|data-sort-value="1" style="background:#fcffa6;|?

|Heath-Brown–Moroz constant{{cite book|url=https://books.google.com/books?id=NuDimaRIVVsC&q=%22Heath-Brown%20and%20Moroz%22&pg=PA29|title=Analytic Number Theory|author=J. B. Friedlander|author2=A. Perelli|author3=C. Viola|author4=D.R. Heath-Brown|author5=H.Iwaniec|author6=J. Kaczorowski|publisher=Springer|year=2002|isbn=978-3-540-36363-7|page=29}}

| $C$

|0.00131 76411 54853 17810 {{MathWorld|Heath-Brown-MorozConstant|Heath-Brown-Moroz Constant}}{{OEIS2C|A118228}}

| $\prod_{p\text{ prime}} \left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right)$

|1999

|data-sort-value="1" style="background:#fcffa6;|?

|MRB constant{{cite book|url=http://www.perfscipress.com/papers/UniversalTOC25.pdf|title=Unified algorithms for polylogarithm, L-series, and zeta variants|author=Richard E. Crandall|publisher=perfscipress.com|year=2012|archive-url=https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf|archive-date=2013-04-30|url-status=usurped}}{{cite arXiv|eprint=0912.3844|class=math.CA|author=RICHARD J. MATHAR|title=NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(I pi x)x^1/x BETWEEN 1 AND INFINITY|year=2010}}{{cite book|url=http://marvinrayburns.com/Original_MRB_Post.html|title=Root constant|author=M.R.Burns|publisher=Marvin Ray Burns|year=1999}}

| $S$

|0.18785 96424 62067 12024 {{MathWorld|MRBConstant|MRB Constant}}MRB constant{{OEIS2C|A037077}}

| $\sum_{n=1}^{\infty} (-1)^n (n^{1/n}-1) = - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \cdots$

|1999

|data-sort-value="1" style="background:#fcffa6;|?

|Prime constant{{Cite book |last=Hardy |first=G. H. |url=https://www.worldcat.org/oclc/214305907 |title=An introduction to the theory of numbers |date=2008 |publisher=Oxford University Press |others=E. M. Wright, D. R. Heath-Brown, Joseph H. Silverman |isbn=978-0-19-921985-8 |edition=6th |location=Oxford |oclc=214305907}}

| $\rho$

|0.41468 25098 51111 66024 {{OEIS2C|A051006}}

| $\sum_{p\text{ prime}} \frac{1}{2^p}= \frac{1}{4} + \frac{1}{8} + \frac{1}{32} + \cdots$

|1999

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|Somos' quadratic recurrence constant{{cite journal|author1=Jesus Guillera|author2=Jonathan Sondow|year=2008|title=Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent|journal=The Ramanujan Journal|volume=16|issue=3|pages=247–270|arxiv=math/0506319|doi=10.1007/s11139-007-9102-0|s2cid=119131640}}

| $\sigma$

|1.66168 79496 33594 12129 {{MathWorld|SomossQuadraticRecurrenceConstant|Somos's Quadratic Recurrence Constant}}{{OEIS2C|A112302}}

| $\prod_{n=1}^\infty n^{{1/2}^n} = \sqrt {1 \sqrt {2 \sqrt{3 \cdots}}} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots$

|1999

|data-sort-value="1" style="background:#fcffa6;|?

|Foias constant{{cite book|url=http://ssmr.ro/gazeta/gma/2007/gma-1-2007.pdf|title=Gazeta Matemetica Seria a revista de cultur Matemetica Anul XXV(CIV)Nr. 1, Constante de tip Euler generalízate|author=Andrei Vernescu|year=2007|page=14}}

| $\alpha$

|1.18745 23511 26501 05459 {{refn|group=Mw|name=Foias|{{MathWorld|FoiasConstant|Foias Constant}}}}{{OEIS2C|A085848}}

| $x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ for }n=1,2,3,\ldots$

Foias constant is the unique real number such that if x₁ = α then the sequence diverges to infinity.

|2000

|data-sort-value="1" style="background:#fcffa6;|?

|Logarithmic capacity of the unit disk{{cite book|url=http://www.people.fas.harvard.edu/~sfinch/csolve/capa.pdf|title=Electrical Capacitance|author=Steven Finch|publisher=Harvard.edu|year=2014|page=1|access-date=2015-10-12|archive-url=https://web.archive.org/web/20160419150944/http://www.people.fas.harvard.edu/~sfinch/csolve/capa.pdf|archive-date=2016-04-19|url-status=dead}}{{cite journal

| last = Ransford | first = Thomas

| doi = 10.1007/BF03321780

| issue = 2

| journal = Computational Methods and Function Theory

| mr = 2791324

| pages = 555–578

| title = Computation of logarithmic capacity

| volume = 10

| year = 2010}}

|0.59017 02995 08048 11302{{MathWorld|LogarithmicCapacity|Logarithmic Capacity}}{{OEIS2C|A249205}}

| $\frac{\Gamma(\tfrac14)^2}{4 \pi^{3/2}}=\frac{\varpi}{\pi\sqrt{2}}$ where $\varpi$ is the lemniscate constant.

| data-sort-value="2003" |Before 2003

|data-sort-value="2" style="background:#ffa6a6;|✗

|data-sort-value="1" style="background:#fcffa6;|?

|Taniguchi constant

|0.67823 44919 17391 97803{{MathWorld|TaniguchisConstant|Taniguchis Constant}}{{OEIS2C|A175639}}

| $\prod_{p\text{ prime}} \left(1 - \frac{3}{p^3}+\frac{2}{p^4}+\frac{1}{p^5}-\frac{1}{p^6}\right)$

| data-sort-value="2005" |Before 2005

|data-sort-value="1" style="background:#fcffa6;|?

Mathematical constants sorted by their representations as continued fractions

The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known.

Name ! Symbol ! Set ! Decimal expansion ! Continued fraction ! Notes
class="wikitable sortable"
Zero \| 0	$\mathbb{Z}$	0.00000 00000	[0; ]
Golomb–Dickman constant \| $\lambda$		0.62432 99885	[0; 1, 1, 1, 1, 1, 22, 1, 2, 3, 1, 1, 11, 1, 1, 2, 22, 2, 6, 1, 1, …]{{OEIS2C\|A225336}}	E. Weisstein noted that the continued fraction has an unusually large number of 1s.{{MathWorld\|Golomb-DickmanConstantContinuedFraction\|Golomb-Dickman Constant Continued Fraction}}
Cahen's constant \| $C_2$	$\mathbb{R} \setminus \mathbb{A}$	0.64341 05463	[0; 1, 1, 1, 2², 3², 13², 129², 25298², 420984147², 269425140741515486², …]{{OEIS2C\|A006280}}	All terms are squares and truncated at 10 terms due to large size. Davison and Shallit used the continued fraction expansion to prove that the constant is transcendental.
Euler–Mascheroni constant \| $\gamma$		0.57721 56649{{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=182}}	[0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, …] {{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=182}}{{OEIS2C\|A002852}}	Using the continued fraction expansion, it was shown that if {{math\|γ}} is rational, its denominator must exceed 10²⁴⁴⁶⁶³.
First continued fraction constant \| $C_1$	$\mathbb{R} \setminus \mathbb{A}$	0.69777 46579	[0; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …]	Equal to the ratio $I_{1}(2)/I_{0}(2)$ of modified Bessel functions of the first kind evaluated at 2.
Catalan's constant \| $G$		0.91596 55942{{sfn\|Borwein\|van der Poorten\|Shallit\|Zudilin\|2014\|p=190}}	[0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, …] {{sfn\|Borwein\|van der Poorten\|Shallit\|Zudilin\|2014\|p=190}}{{OEIS2C\|A014538}}	Computed up to {{val\|4851389025}} terms by E. Weisstein.{{MathWorld\|CatalansConstantContinuedFraction\|Catalan's Constant Continued Fraction}}
One half \| {{sfrac\|1\|2}}	$\mathbb{Q}$	0.50000 00000	[0; 2]
Prouhet–Thue–Morse constant \| $\tau$	$\mathbb{R} \setminus \mathbb{A}$	0.41245 40336	[0; 2, 2, 2, 1, 4, 3, 5, 2, 1, 4, 2, 1, 5, 44, 1, 4, 1, 2, 4, 1, …]{{OEIS2C\|A014572}}	Infinitely many partial quotients are 4 or 5, and infinitely many partial quotients are greater than or equal to 50.{{cite journal \|last1=Bugeaud \|first1=Yann \|last2=Queffélec \|first2=Martine \|title=On Rational Approximation of the Binary Thue-Morse-Mahler Number \|journal=Journal of Integer Sequences \|date=2013 \|volume=16 \|issue=13.2.3 \|url=https://cs.uwaterloo.ca/journals/JIS/VOL16/Bugeaud/bugeaud3.html}}
Copeland–Erdős constant \| $\mathcal{C}_{CE}$	$\mathbb{R} \setminus \mathbb{Q}$	0.23571 11317	[0; 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, …]{{OEIS2C\|A030168}}	Computed up to {{val\|1011597392}} terms by E. Weisstein. He also noted that while the Champernowne constant continued fraction contains sporadic large terms, the continued fraction of the Copeland–Erdős Constant do not exhibit this property.{{MathWorld\|Copeland-ErdosConstantContinuedFraction\|Copeland–Erdős Constant Continued Fraction}}
Base 10 Champernowne constant \| $C_{10}$	$\mathbb{R} \setminus \mathbb{A}$	0.12345 67891	[0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, {{val\|4.57540e165\|fmt=none}}, 6, 1, …] {{OEIS2C\|A030167}}	Champernowne constants in any base exhibit sporadic large numbers; the 40th term in $C_{10}$ has 2504 digits.
One \| 1	$\mathbb{N}$	1.00000 00000	[1; ]
Phi, Golden ratio \| $\varphi$	$\mathbb{A}$	1.61803 39887{{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=185}}	[1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …] {{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=186}}	The convergents are ratios of successive Fibonacci numbers.
Brun's constant \| $B_2$		1.90216 05831	[1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, …]	The n^th roots of the denominators of the n^th convergents are close to Khinchin's constant, suggesting that $B_2$ is irrational. If true, this will prove the twin prime conjecture.{{cite arXiv \|last=Wolf \|first=Marek \|date=22 February 2010 \|title=Remark on the irrationality of the Brun's constant \|eprint=1002.4174 \|class=math.NT}}
Square root of 2 \| $\sqrt 2$	$\mathbb{A}$	1.41421 35624	[1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …]	The convergents are ratios of successive Pell numbers.
Two \| 2	$\mathbb{N}$	2.00000 00000	[2; ]
Euler's number \| $e$	$\mathbb{R} \setminus \mathbb{A}$	2.71828 18285{{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=176}}	[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, …] {{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=179}}{{OEIS2C\|A003417}}	The continued fraction expansion has the pattern [2; 1, 2, 1, 1, 4, 1, ..., 1, 2n, 1, ...].
Khinchin's constant \| $K_0$		2.68545 20011{{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=190}}	[2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, …] {{sfn\|Cuyt\|Petersen\|Verdonk\|Waadeland\|2008\|p=191}}{{OEIS2C\|A002211}}	For almost all real numbers x, the coefficients of the continued fraction of x have a finite geometric mean known as Khinchin's constant.
Three \| 3	$\mathbb{N}$	3.00000 00000	[3; ]
Pi \| $\pi$	$\mathbb{R} \setminus \mathbb{A}$	3.14159 26536	[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, …] {{OEIS2C\|A001203}}	The first few convergents (3, 22/7, 333/106, 355/113, ...) are among the best-known and most widely used historical approximations of {{math\|π}}.

Sequences of constants

class="wikitable sortable"
Name ! Symbol ! Formula ! Year ! Set
Harmonic number \| $H_n$ \| $\sum^n_{k=1}\frac{1}{k}$ \| data-sort-value="-400" \| Antiquity \|data-sort-value="3" \| $\mathbb{Q}$
Gregory coefficients \| $G_n$ \| $\frac 1 {n!} \int_0^1 x(x-1)(x-2)\cdots(x-n+1)\, dx = \int_0^1 \binom x n \, dx$ \| 1670 \| data-sort-value="3" \| $\mathbb{Q}$
Bernoulli number \| $B^\pm_n$ \| $\frac{t}{2} \left( \operatorname{coth} \frac{t}{2} \pm 1 \right) = \sum_{m=0}^\infty \frac{B^{\pm{}}_m t^m}{m!}$ \| 1689 \| data-sort-value="3" \| $\mathbb{Q}$
Hermite constants{{cite web \| url=https://mathworld.wolfram.com/HermiteConstants.html \| title=Hermite Constants }} \| $\gamma_{n}$ \| For a lattice L in Euclidean space Rⁿ with unit covolume, i.e. vol(Rⁿ/L) = 1, let λ{{Sub\|1}}(L) denote the least length of a nonzero element of L. Then √γ{{Subscript\|n}}n is the maximum of λ{{Sub\|1}}(L) over all such lattices L. \| data-sort-value="1822" \| 1822 to 1901 \| data-sort-value="7" \| $\mathbb{R}$
Hafner–Sarnak–McCurley constant{{cite book\|url=https://books.google.com/books?id=007-3SM9QmYC&q=0.607927101854026628663276779&pg=PA270\|title=Process Algebra and Probabilistic Methods.\|author1=Holger Hermanns\|author2=Roberto Segala\|publisher=Springer-Verlag\|year=2000\|isbn=978-3-540-67695-9\|page=270}} \| $D(n)$ \| $D(n)= \prod^\infty_{k=1}\left\{1-\left[1-\prod^n_{j=1}(1-p_k^{-j}) \right]^2 \right\}$ \| data-sort-value="1883" \|1883{{MathWorld\|RelativelyPrime\|Relatively Prime}} \| data-sort-value="7" \| $\mathbb{R}$
Stieltjes constants \| $\gamma_n$ \| ${\frac {(-1)^{n}n!}{2\pi }}\int _{0}^{{2\pi }}e^{{-nix}}\zeta \left(e^{{ix}}+1\right)dx.$ \| data-sort-value="1894"\|before 1894 \| data-sort-value="7" \| $\mathbb{R}$
Favard constants{{cite web \| url=https://mathworld.wolfram.com/FavardConstants.html \| title=Favard Constants }} \| $K_{r}$ \| $\frac{4}{\pi}\sum_{n = 0}^\infty \left(\frac{(-1)^n}{2n+1} \right)^{\!r+1}=\frac{4}{\pi}\left( \frac{(-1)^{0(r+1)}}{1^r}+\frac{(-1)^{1(r+1)}}{3^r}+\frac{(-1)^{2(r+1)}}{5^r}+\frac{(-1)^{3(r+1)}}{7^r}+\cdots\right)$ \| data-sort-value="1902" \| 1902 to 1965 \| data-sort-value="7" \| $\mathbb{R}$
Generalized Brun's Constant \| $B_{n}$ \| ${\sum\limits_p(\frac1{p}+\frac1{p+n})}$ where the sum ranges over all primes p such that p + n is also a prime \| data-sort-value="1919" \|1919{{OEIS2C\|A065421}} \| data-sort-value="7" \| $\mathbb{R}$
Champernowne constants \| $C_{b}$ \|Defined by concatenating representations of successive integers in base b. $C_b=\sum^\infty_{n=1}\frac{n}{b^{\left(\sum^n_{k=1}\lceil\log_b(k+1)\rceil\right)}}$ \|1933 \| data-sort-value="5" \| $\mathbb{R} \setminus \mathbb{A}$
Lagrange number \| $L(n)$ \| $\sqrt{9-\frac{4}{{m_n}^2}}$ where $m_n$ is the nth smallest number such that $m^2+x^2+y^2=3mxy\,$ has positive (x,y). \| data-sort-value="1957"\|before 1957 \| data-sort-value="4" \| $\mathbb{A}$
Feller's coin-tossing constants \| $\alpha_k,\beta_k$ \| $\alpha_k$ is the smallest positive real root of $x^{k+1}=2^{k+1}(x-1),\beta_k=\frac{2-\alpha_k}{k+1-k\alpha_k}$ \| 1968 \| data-sort-value="4" \| $\mathbb{A}$
Stoneham number \| $\alpha_{b,c}$ \| $\sum_{n=c^k>1} \frac{1}{b^nn} = \sum_{k=1}^\infty \frac{1}{b^{c^k}c^k}$ where b,c are coprime integers. \| 1973 \| data-sort-value="6" \| $\mathbb{R} \setminus \mathbb{A}$
Beraha constants \| $B(n)$ \| $2+2\cos\left(\frac{2\pi}{n}\right)$ \| 1974 \| data-sort-value="7" \| $\mathbb{A}$
Chvátal–Sankoff constants \| $\gamma_k$ \| $\lim_{n\to\infty}\frac{E[\lambda_{n,k}]}{n}$ \| 1975 \| data-sort-value="7" \| $\mathbb{R}$
Hyperharmonic number \| $H^{(r)}_n$ \| $\sum^n_{k=1}H^{(r-1)}_k$ and $H^{(0)}_n=\frac{1}{n}$ \| 1995 \|data-sort-value="3" \| $\mathbb{Q}$
Gregory number \| $G_x$ \| $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}=\arccot(x)$ for rational x greater than or equal to one. \| data-sort-value="1996"\|before 1996 \| data-sort-value="7" \| $\mathbb{R} \setminus \mathbb{A}$
Metallic mean \| \| $\frac{n+\sqrt{n^2+4}}{2}$ \|data-sort-value="1998" \| before 1998 \|data-sort-value="4" \| $\mathbb{A}$

class="wikitable sortable"

Name

! Symbol

! Formula

! Year

! Set

Harmonic number

| $H_n$

| $\sum^n_{k=1}\frac{1}{k}$

| data-sort-value="-400" | Antiquity

|data-sort-value="3" | $\mathbb{Q}$

Gregory coefficients

| $G_n$

| $\frac 1 {n!} \int_0^1 x(x-1)(x-2)\cdots(x-n+1)\, dx = \int_0^1 \binom x n \, dx$

| 1670

| data-sort-value="3" | $\mathbb{Q}$

Bernoulli number

| $B^\pm_n$

| $\frac{t}{2} \left( \operatorname{coth} \frac{t}{2} \pm 1 \right) = \sum_{m=0}^\infty \frac{B^{\pm{}}_m t^m}{m!}$

| 1689

| data-sort-value="3" | $\mathbb{Q}$

Hermite constants{{cite web | url=https://mathworld.wolfram.com/HermiteConstants.html | title=Hermite Constants }}

| $\gamma_{n}$

| For a lattice L in Euclidean space Rⁿ with unit covolume, i.e. vol(Rⁿ/L) = 1, let λ{{Sub|1}}(L) denote the least length of a nonzero element of L. Then √γ{{Subscript|n}}n is the maximum of λ{{Sub|1}}(L) over all such lattices L.

| data-sort-value="1822" | 1822 to 1901

| data-sort-value="7" | $\mathbb{R}$

Hafner–Sarnak–McCurley constant{{cite book|url=https://books.google.com/books?id=007-3SM9QmYC&q=0.607927101854026628663276779&pg=PA270|title=Process Algebra and Probabilistic Methods.|author1=Holger Hermanns|author2=Roberto Segala|publisher=Springer-Verlag|year=2000|isbn=978-3-540-67695-9|page=270}}

| $D(n)$

| $D(n)= \prod^\infty_{k=1}\left\{1-\left[1-\prod^n_{j=1}(1-p_k^{-j}) \right]^2 \right\}$

| data-sort-value="1883" |1883{{MathWorld|RelativelyPrime|Relatively Prime}}

| data-sort-value="7" | $\mathbb{R}$

Stieltjes constants

| $\gamma_n$

| ${\frac {(-1)^{n}n!}{2\pi }}\int _{0}^{{2\pi }}e^{{-nix}}\zeta \left(e^{{ix}}+1\right)dx.$

| data-sort-value="1894"|before 1894

| data-sort-value="7" | $\mathbb{R}$

Favard constants{{cite web | url=https://mathworld.wolfram.com/FavardConstants.html | title=Favard Constants }}

| $K_{r}$

| $\frac{4}{\pi}\sum_{n = 0}^\infty \left(\frac{(-1)^n}{2n+1} \right)^{\!r+1}=\frac{4}{\pi}\left( \frac{(-1)^{0(r+1)}}{1^r}+\frac{(-1)^{1(r+1)}}{3^r}+\frac{(-1)^{2(r+1)}}{5^r}+\frac{(-1)^{3(r+1)}}{7^r}+\cdots\right)$

| data-sort-value="1902" | 1902 to 1965

| data-sort-value="7" | $\mathbb{R}$

Generalized Brun's Constant

| $B_{n}$

| ${\sum\limits_p(\frac1{p}+\frac1{p+n})}$ where the sum ranges over all primes p such that p + n is also a prime

| data-sort-value="1919" |1919{{OEIS2C|A065421}}

| data-sort-value="7" | $\mathbb{R}$

Champernowne constants

| $C_{b}$

|Defined by concatenating representations of successive integers in base b.

$C_b=\sum^\infty_{n=1}\frac{n}{b^{\left(\sum^n_{k=1}\lceil\log_b(k+1)\rceil\right)}}$

|1933

| data-sort-value="5" | $\mathbb{R} \setminus \mathbb{A}$

Lagrange number

| $L(n)$

| $\sqrt{9-\frac{4}{{m_n}^2}}$ where $m_n$ is the nth smallest number such that $m^2+x^2+y^2=3mxy\,$ has positive (x,y).

| data-sort-value="1957"|before 1957

| data-sort-value="4" | $\mathbb{A}$

Feller's coin-tossing constants

| $\alpha_k,\beta_k$

| $\alpha_k$ is the smallest positive real root of $x^{k+1}=2^{k+1}(x-1),\beta_k=\frac{2-\alpha_k}{k+1-k\alpha_k}$

| 1968

| data-sort-value="4" | $\mathbb{A}$

Stoneham number

| $\alpha_{b,c}$

| $\sum_{n=c^k>1} \frac{1}{b^nn} = \sum_{k=1}^\infty \frac{1}{b^{c^k}c^k}$ where b,c are coprime integers.

| 1973

| data-sort-value="6" | $\mathbb{R} \setminus \mathbb{A}$

Beraha constants

| $B(n)$

| $2+2\cos\left(\frac{2\pi}{n}\right)$

| 1974

| data-sort-value="7" | $\mathbb{A}$

Chvátal–Sankoff constants

| $\gamma_k$

| $\lim_{n\to\infty}\frac{E[\lambda_{n,k}]}{n}$

| 1975

| data-sort-value="7" | $\mathbb{R}$

Hyperharmonic number

| $H^{(r)}_n$

| $\sum^n_{k=1}H^{(r-1)}_k$ and $H^{(0)}_n=\frac{1}{n}$

| 1995

|data-sort-value="3" | $\mathbb{Q}$

Gregory number

| $G_x$

| $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}=\arccot(x)$ for rational x greater than or equal to one.

| data-sort-value="1996"|before 1996

| data-sort-value="7" | $\mathbb{R} \setminus \mathbb{A}$

Metallic mean

| $\frac{n+\sqrt{n^2+4}}{2}$

|data-sort-value="1998" | before 1998

|data-sort-value="4" | $\mathbb{A}$

Notes

References

= Site MathWorld Wolfram.com =

= Site OEIS.org =

= Site OEIS Wiki =

Bibliography

{{cite book|last1=Arndt|first1=Jörg|last2=Haenel|first2=Christoph|title=Pi Unleashed|publisher=Springer-Verlag|year=2006|isbn=978-3-540-66572-4 |url=https://books.google.com/books?id=QwwcmweJCDQC|access-date=2013-06-05}} English translation by Catriona and David Lischka.
{{Citation|last=Jensen|first=Johan Ludwig William Valdemar|title=Note numéro 245. Deuxième réponse. Remarques relatives aux réponses du MM. Franel et Kluyver|journal=L'Intermédiaire des Mathématiciens|volume=II|pages=346–347|year=1895}}
{{cite book|title=Handbook of Continued Fractions for Special Functions|author1-first=Annie A.M.|author1-last=Cuyt|author1-link=Annie Cuyt|author2-first=Vigdis|author2-last=Petersen|author3-first=Brigitte|author3-last=Verdonk|author4-first=Haakon|author4-last=Waadeland|author5-first=William B.|author5-last=Jones|publisher=Springer Science + Business Media|year=2008|isbn=9781402069499|chapter=Mathematical constants |location=Dordrecht, Netherlands}}
{{cite book|title=Neverending Fractions: An Introduction to Continued Fractions|volume=23|series=Australian Mathematical Society Lecture Series|issn=0950-2815|author1-first=Jonathan|author1-last=Borwein|author2-first=Alf|author2-last=van der Poorten|author3-first=Jeffrey|author3-last=Shallit|author4-first=Wadim|author4-last=Zudilin|location=Cambridge, United Kingdom|publisher=Cambridge University Press|year=2014|isbn=9780521186490}}

External links

[https://web.archive.org/web/20181030072352/http://isc.carma.newcastle.edu.au/standard Inverse Symbolic Calculator, Plouffe's Inverter]
[https://mathworld.wolfram.com/topics/Constants.html Constants – from Wolfram MathWorld]
[https://oeis.org/wiki/Index_to_OEIS On-Line Encyclopedia of Integer Sequences (OEIS)]
[https://web.archive.org/web/20120912131952/http://www.people.fas.harvard.edu/~sfinch/ Steven Finch's page of mathematical constants]
[http://numbers.computation.free.fr/Constants/constants.html Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms]

mathematical constants

Constants

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Category:Continued fractions